who plays grant on secret life of the american teenager

Grant Harvey portrays Grant, Griffin's awkward but engaging cousin, who is not gay and is interested in Ashley. He is put up to a blind date with Ashley by Griffin, and finds himself attracted to her. At first, George isn't concerned, thinking that since Grant is related to Griffin, he must be gay, too. He is taken aback to discover that Grant is not gay, but decides to trust Ashley not to make the same mistake that Amy did. He wants to have sex with Ashley. After a party held by Leo and Ben, Grant finds interest in Grace, and is now dating her. He and Grace stay abstinent through their summer at Med Camp, and have sex after school starts when Grant's parents are out of town. Grant then told Grace that he loved her. Later, Grant's parents come to the Bowman-Tseguay residence and it is found that Grant's father is quite old, but charms the hearts of both Grace and Kathleen..

List of The Secret Life of the American Teenager characters

The Secret Life of the American Teenager is a television series created by Brenda Hampton. It first premiered on ABC Family on July 1, 2008 and ran until June 3, 2013.[1] The show features a regular cast of characters, which began with eleven people in its first season. Since then, characters have left the show, with new main characters having both been written in and out of the series. In addition, Secret Life features multiple guest stars each week, some having larger roles than others.

The plot focuses on the character of Amy Juergens after becoming accidentally pregnant at band camp. It explores how the pregnancy affects her, her peers, and her family. After her sister starts high school, Amy finds how virtually everyone at school carries a secret or an unexpected problem. Amy is the mother of John Juergens.

Portrayed by Shailene Woodley, Amy gets pregnant after a one-night stand at band camp before her freshman year of high school. At the beginning of the series, she is 15 years old. Upon entering high school, Amy begins a relationship with Ben Boykewich (also 15), a supportive classmate with whom she falls in love. She confesses her pregnancy to her two best friends, Madison and Lauren, who accidentally spread the rumor that Amy had sex with Ricky. During this time, Amy's 13-year-old sister Ashley discovers her pregnancy due to Amy's recent weight gain and erratic behavior, but promises to keep her secret from their parents. Ben proposes to Amy after finding out, because he genuinely loves her, and feels he would be a better father than Ricky due to his family's financial stability. After Amy tells her parents, she contemplates having an abortion, as she is afraid of her peers' perceptions. She changes her mind, but is still adamant about not returning to school. Ricky reaches out to Amy during this time, saying that he wants to be involved with what happens to the baby. Amy plans to go live with her grandmother Mimsy, but is unable to go after discovering that Mimsy is suffering from Alzheimer's disease, and is moving into assisted care living. Amy returns to school, but is uncomfortable with being known as "the pregnant girl".

Halfway through her pregnancy, Amy's mother Anne informs her that in order to keep the baby, she will have to find a job and daycare. Anne intends to get a job to replace the loss of her husband George's income as they prepare for divorce. Amy is surprised, since she assumed that her mother would stay home and look after the baby, as she had with her daughters. As a result, Amy and Ben get married using fake IDs, but they learn afterwards that the marriage was void since they were both underage. Amy then decides on adoption, and discovers that her father's longtime employee Donovan and his husband Leon want to adopt the baby. The adoption fails due to Ricky's interference, and she ultimately decides to keep the baby due to the love and support of her family and friends.

After Amy decides to keep the baby, Grace and Adrian throw her a baby shower, where Amy then goes into labor. While in the hospital, Amy reprimands Ricky for getting her pregnant, but then realizes that she was equally responsible for what had happened. She gives birth to their son, John, whom she lets Ashley name, and begins to struggle with motherhood.

After breaking up with Ben during her sophomore year, Amy briefly dates Jimmy, the son of her mother's ex-boyfriend, but their relationship ends after he finds a condom in her purse. Not knowing this at first, Amy thinks that Jimmy broke up with her because she was a bad kisser, and asks Ricky to kiss her just to be sure. Adrian finds out about the kiss, and sleeps with Ben in order to get back at both of them (however, Adrian believed it was more than a kiss until Ricky informs her after Adrian and Ben's one-night-stand.) Amy and Ben quickly reconcile and get back together around the end of the year.

After being accepted into a summer music program in New York, Amy decides to go but is surprised to learn that the program is for teen mothers. During this time, Ben reveals to Amy that Adrian had gotten pregnant from their one-night stand, and that he had been keeping her pregnancy from Amy for several weeks. After breaking up with Ben, she develops feelings for Ricky when he comes to visit. She tells him that if he really wants to be with her, he has to stop sleeping around,and get tested for any sexually transmitted diseases or infections.

At the beginning of season four, Amy and Ricky are together and are trying to be a real family for their son. After the stillborn death of Ben and Adrian's daughter, Amy and Ricky begin a sexual relationship. Three months later, Amy moves herself and John into Ricky's little apartment over the butcher shop where he works. Amy decides she wants to marry Ricky, but he thinks she's moving too fast. Later he proposes at their graduation, where he is also valedictorian. At a graduation party, Ricky kisses Adrian one last time; something Amy allowed. The next day, Ricky is surprised that Amy isn't in a hurry to marry, but is content with just being engaged until she feels the time is right for them to marry. Later in the season, Amy thinks she is pregnant again and becomes very moody. Although she finds out that she is not pregnant, she is still irritable. Ricky takes her back to where they first met and Amy begins to become a little more happy and appreciative of Ricky, and more excited about his proposal to her. Shortly after Amy discovers her mother is a lesbian, she tells Ricky that they should just run off and get married, to which Ricky agrees. Amy tells everyone that Ricky and her eloped in the season 5 premiere, keeping the fact they changed their minds at the last minute and are in fact not married a secret. Eventually she breaks off the relationship and goes to college in New York, leaving John with Ricky.

Portrayed by Daren Kagasoff, Ricky Underwood is the lead male character. His father, Bob, is a drug addict who beat Ricky's mother Nora and sexually abused Ricky as a young child. His mother was both a drug addict and an alcoholic who never helped him out of fear. Ricky was taken away from his parents after the abuse came to light, and put into foster care. As a teenager, Ricky attended Ulysses S. Grant High School, where he was the drummer in the high school marching band and had a reputation of being a promiscuous bad boy. He used to see a therapist, Lauren's father Dr. Ken Fields, who he occasionally visits for advice as an adult. The summer before Ricky's sophomore year, he impregnated Amy Juergens after a one-night stand at band camp, finding out about her pregnancy a few months later. Despite his misgivings over being a good father, Ricky is shown to love and care for his son John. He and Amy go on a date in the fall finale of season 3 and she makes him get tested before considering having sex with him. Ricky tests disease-free, and chooses to not have sex with anyone other than Amy. Their first time having sex occurred in the wake of dealing with the news of Ben and Adrian's stillborn daughter. Amy and John soon move in with Ricky. Amy finds messages left by Adrian, after telling her she's in love with Ricky. Amy gets caught by Ricky, with him stating they should spend some time apart if she can't trust him. Ricky eventually apologizes to Amy and they get back together. Amy tries to get Ricky to propose by doing "wild" things such as giving him a milkshake and a bath. Ricky ends up being the Valedictorian, and at the end of his speech he proposes to Amy. At the graduation party Amy allows Ricky to kiss Adrian one last time to give closure to her. Ricky wants to know when Amy wants to get married, and is taken aback when Amy doesn't seem to be in a hurry to plan their wedding. Amy then has a pregnancy scare, and Ricky is supportive and takes Amy to band camp so she can be happy. Amy told everyone that Ricky and her eloped in the season 5 premiere even though they pulled out at the last minute. Eventually Amy breaks up with him and leaves John in his care while she goes to New York to attend college.

Portrayed by Francia Raisa, Adrian is the daughter of Ruben Enriquez and Cindy Lee, and the ex-wife of Ben. She is 20 years old. Adrian is both book smart and street smart, hard-edged and emotional. Although she is a straight-A student and a majorette, she has a reputation for being a drama queen and the "school slut". She also has strong feelings for Ricky despite claiming she doesn't anymore since they stopped speaking to each other. Adrian grew up never knowing who her father was, until she went on a search to find him. Her father ended up marrying her mother after 16 years of being apart from each other. Adrian and her parents now live next door to the Juergens family. Her mother is a flight attendant and her father is a District Attorney. Like Ricky, Adrian is also known to use sex to deal with pain. In the episode "Be My, Be My Baby", she reveals that she first had sex when she was fifteen, with her childhood best friend Antonio, who was moving away in order to get cancer treatments. Adrian was infuriated after she found out that Ricky kissed Amy, believing that it went beyond kissing, even though it was a mostly innocent encounter. Adrian had a one-night-stand with Ben in retaliation, and ended up becoming pregnant with his child. She had her mind set on abortion, but she eventually backed out and decided to keep the baby. Adrian's decision to keep the baby received a lot of positive support from her father and even Amy, who had called her to let her know that she was giving Adrian the same offer of a friendship between them that she had given her in the past, because their children might end up becoming friends. Adrian later finds out that she is having a baby girl, which both she and Ben are excited about, and she and Ben later get married. Adrian gives birth to their daughter Mercy, who is tragically stillborn due to heart failure. Adrian and Ben are both absolutely devastated by Mercy's death. After this, Ben realizes he no longer loves Adrian, and that he may never have truly loved her. Ben decides that he wants a divorce. When she finds this out, Adrian tries to get pregnant again, believing that they will fall back in love and be happy again if she has another baby. When this doesn't work, she decides he should leave. After Ben left, Adrian realized she still loved Ricky, so she decided to date a guy named Dante in an attempt to make Ricky jealous. In the process, she meets Dante's brother, Omar, and begins dating him, because Dante left the country without an explanation. But Ricky had other plans - he ended up proposing to Amy at their graduation. Adrian wants one last kiss from Ricky, to see if she still has feelings for him. At the graduation party, she receives the kiss and is happy to discover that the kiss leaves her unmoved; however, Omar is at the party and is offended by Adrian kissing Ricky, and leaves. Disconsolate, Adrian has sex with Henry. The next day, she realizes that she has made a mistake, and repeatedly calls Omar, who does not answer her calls. To her surprise, Dante arrives back from his semester abroad. When she tells him that she has been seeing his brother, he breaks up with her. Adrian and her best friend Grace are fed up with boys, and decide to enroll in summer school together. Shortly after, Adrian gets a letter in the mail, stating that she is legally divorced from Ben. She then completes summer school and shows signs of still being in love with Ricky. She falls back in love with Omar, but denies his proposal of marriage, wanting to wait until her schooling is complete.

Portrayed by Ken Baumann, Benjamin "Ben" Boykewich 15-year-old son of Leo Boykewich, is Amy's high school boyfriend and first love. He meets Amy after his best friend Alice points her out one day at school, and they begin dating and fall in love. He offers to marry Amy when he finds out she's pregnant, but she declined his offer at the time. When Amy's mother Anne, tells her that she must support her baby on her own, she changed her mind and decides to marry Ben, as his family is financially stable. Amy and Ben get married with fake ID's, but discoverver that their marriage is null and void because they are both minors. They eventually break up after Amy's baby is born and Ben can't handle seeing her bond with Ricky. Adrian finds out she is pregnant with Ben's baby after a one-night stand essentially ruining Ben's chances of a relationship with Amy and they eventually get together. They marry and move in together before their baby is born with the financial support of Ben's father. After their baby is born stillborn Ben can't handle Adrian anymore and decides to divorce her against her wishes. At the end of the series, Ben follows Amy to New York, only to give up on her after Amy realizes that she was never really in love with Ben, and he was never really in love with her. The two then go their separate ways.

Portrayed by India Eisley, Ashley Juergens is the youngest daughter of Anne and George, and Amy's younger sister. She is mature, observant, and sarcastic, tending to speak in a low, monotone voice. Ashley is the first member in the Juergens family to learn of Amy's pregnancy. She is often forgotten by her family and remarks that she could get away with anything. However, Ashley's main concern is keeping her family together. Ashley believed that Amy's baby would reunite her dividing family and worked hard to discourage Amy from adoption. After the baby was born, she named her nephew John since she thought it was simple and classic. During the third season she developed feelings for Ricky. She stays away from Ricky, for benefit of Amy and Ricky, but is told to back down by Amy so that she and Ricky can see if they can try to be a couple. Ashley passes her GED after a brief stint in home-schooling and travels across the US with her new friend, Toby. They end up broke in Florida and stay with his grandmother, earning money with various part-time jobs. Ashley returns home the day after Ricky's graduation and announces that she will be attending college in Florida in the fall. In season 5, Ashley's relationship with Toby has progressed into a sexual relationship. Her father is very upset once hearing this, but Ashley explains that they are in love and practicing safe-sex. After coming back from a trip to Europe with her mother, she finds out that she was accepted to a cooking school in Italy. Both George and Anne say no to the idea, so she ends up running away with the help of her grandmother Mimsy, who gives her ten thousand dollars.

Portrayed by Greg Finley II, Jack Pappas is a college freshman and quarterback on the football team. His stepfather, Reverend Stone, is the minister of the church where he and Grace first met. He cheats on Grace in the first episode when he has oral sex with Adrian, and is then caught kissing her at the school dance. Grace eventually forgives him, and they start to date in secret because of her parent's disapproval. To Jack's dismay, Ricky pretends to be dating Grace as a cover for her parent's. Their relationship ends again when a security camera catches Ricky saving Grace from two men after Jack left her in a bad part of town. He is shown to be clearly jealous over Ricky, which prompts him to tell Grace that he only started dating her because his step-father asked him to. He eventually breaks up with Grace and moves in with Tom in Grace's family's guest house, even though he still loves Grace. He later dates Madison and they break up after summer vacation. Jack and Madison reunite, and although they are back together, Madison becomes very jealous that Jack is living with Grace's family. He moves out of the guest house and into the big house (where Grace lives) because Tom's new girlfriend and her children move into the guest house with Tom. Jack's room is next to Grace's which makes Madison even more nervous about their relationship. Later on, Jack and Madison break up, because he is still in love with Grace. Jack is chosen to give the invocation at the graduation ceremony, and Grace helps him write it. At the end of season 4 they share a kiss to see if they still have feelings for each other. The kiss is captured on a cell phone, and the picture is sent to Grace's current boyfriend, Daniel. Jack is jubilant when Grace's boyfriend breaks up with her, but Grace's mother suggests that since he is going to college in a few months, perhaps he'd be better off just being friends with Grace and taking advantage of new college experiences. He tries to date by sleeping with a girl named Clementine, who is an old friend of Ricky's, but realizes that he still wants to be with Grace. After they get back together, Grace discovers his recent relationship with Clementine, and has trouble trusting him. Jack is in critical condition after a pimp beat him with a baseball bat in his dorm room for paying an underage prostitute without sex and helping her escape. Jack eventually ends up marrying Madison. They also move to New York. Jack becomes a coach at St. Francis

Portrayed by Megan Park, Grace Bowman is the biological daughter of Marshall and Kathleen Bowman and the younger sister of the adopted Tom Bowman. Grace is 18 years old. She is in 12th grade, and an ex-cheerleader. At the beginning of the show, Grace was a devout religious person and does her best to be stay true to her religion. Originally, she was in a relationship with Jack, but they had a lot of disagreements over whether or not to have sex. Grace believed in waiting till marriage, and even wore a promise ring to prove it. She and Jack later break up after he has oral sex with Adrian. She briefly becomes involved with Ricky, but breaks up with him after discovering that he's still sleeping with Adrian. Grace and Jack get back together when Amy has John. In the second season opener, she and Jack decide to have sex. She quickly regrets her decision after the sudden death of her father. She later on becomes involved with Grant, the cousin of Griffin. Grant and Grace bond over their shared desire to become doctors, and strengthen that bond over a summer at MED camp. In her endeavors to become a doctor, she visits Africa with her doctor step-father, where she cheats on Grant with Daniel, a college student. Grant and Grace later break up and she begins to date Daniel, but their relationship isn't smooth due to his greater maturity. Grace becomes jealous of Daniel's ex-girlfriend at the graduation party and Daniel leaves. Grace and Jack share a kiss the next morning after the party, which is captured on a cell phone by Daniel's ex-girlfriend, Raven. Raven texts the picture to Daniel, and he breaks up with Grace, realizing that she still has feelings for Jack. Grace later confesses to Adrian that she thinks she may still be in love with Jack. She and Jack end their engagement and she moves to New York and becomes a doctor.

Portrayed by Mark Derwin, George Juergens is the estranged husband of Anne Juergens, the father of Amy, Ashley and Robbie Juergens, and the maternal grandfather of John Juergens. George is a comically blunt, somewhat immature and often oblivious man, but one who loves his family and tries hard to protect them and keep them together. His first wife was Kathleen Bowman, a woman who married him for sex. George, a furniture salesman, met Anne while she was in college. He and Anne eloped shortly after discovering Anne was pregnant with Amy. Two years later, they had Ashley. It is later found out that he cheated on Anne with other women. The two get a divorce and remarried and separate again. He also has another son with Anne, Robie. He currently lives at his children's childhood home with his dog. When everyone moves out, he invites Ricky's mother, Nora, to move in with him as a roommate. She moves into Ashley's garage bedroom. George and Anne still feel a spark for each other, but Anne seems intent on seeing the divorce go through. After George realizes Anne really is gay and he has no more feelings for her, he starts to date his first wife Kathleen (Grace and Tom's mother) again. They realize they still have their spark and that they are still in love.

Portrayed by Molly Ringwald, Anne Juergens is the daughter of Mimsy and Robert, the divorced wife of George Juergens, the mother of Amy, Ashley and Robbie Juergens and the maternal grandmother of John Juergens. She is a responsible, practical, and naturally independent woman who tries to install the same virtues in her daughters. Anne met George while she was majoring in Women's Studies at college. When Anne discovered she had become pregnant with Amy, she reluctantly dropped out of college, married George and became a wife. Two years later, she had Ashley, and another 14 years after that, she had Robbie. She and George separated after she became tired of his womanizing and realized that she was not happy in the marriage. She dated an architect for a while, and they planned to marry when she became pregnant, thinking it was his child; he later confessed that he could not have children, and she realized that Robbie was George's son. She lived with her mother for a while after her separation from George, but when her mother went into a home for Alzheimer's patients, she was on her own, and began to see a high school sweetheart for companionship, but the relationship didn't go anywhere. She and George made an attempt to get back together and she took over the design portion of his furniture business, but again she finds poorly-hidden evidence that he was unfaithful, and resumed divorce proceedings. In season 5, after George spreads the truth as a rumor around town, Anne Juergens comes out to her family as a lesbian. She walks in her house one day when Nora (Ricky's birth mother) was having an AA meeting with all lesbians attending. Anne gets to know one of them closely and invited her to stay the night. They plan to go out on a date.

Steve Schirripa portrays Leo Boykewich, Ben's widowed father. He owns the local butcher shop, and is known as "The Sausage King". Leo is one of the first people to suspect Amy's pregnancy due to her huge appetite and nausea. He even supported Ben's decision to marrying Amy since he met Ben's mother when they were in high school. He's usually portrayed as the voice of reason for many of the characters on the shows. Such as when he tells Ben off for believing that he can support Amy's baby with his money. He gives Ben and Ricky jobs at the butcher shop as a way to help support Amy. In the second season, Leo begins to date a woman named Betty, who is the prostitute Tom had once hired. We later learn from Betty that she was very upfront about her profession the first day she introduced herself to Leo, because she was afraid of embarrassing him. He later proposes to Betty, but she explains that she may still be married to her ex. He promises to hunt down her husband, who turns out to be dead, and they get married in an elaborate ceremony. Leo takes Ricky under his wing by allowing him to live in the upstairs apartment. He is upset when Ben and Adrian discover they are having a baby, and tries to caution Ben from marrying Adrian just because she is pregnant. Ben is insistent, however, so Leo purchases a condo for the newlyweds. When Ben is ambivalent about being married, Leo sternly tells him that he made the choice, and he now has to make the best of it. When the baby is stillborn, Leo tearfully breaks the news to Ben and Adrian's friends at the hospital, and then later supports Ben's decision to get a divorce. In Season 4, Leo questions whether or not he wants to be married to Betty anymore when he suspects that his longtime assistant, Camille, is in love with him. Even so, Leo decides to stick with the marriage because he believes that is the right thing to do. Betty later decides that she wants a divorce and Leo agrees to it. He later sends Camille flowers and a bracelet and invites her out to dinner. While talking in the car on the way to dinner Camille kisses Leo, and the two are later seen together at graduation. They get married in the fifth season, and decide to adopt a young girl who was the under-aged prostitute that Jack helped.

The following is a list of characters that are, or at one time were, a recurring guest on the series.

Anne Ramsay portrays Nora Underwood, Ricky's biological mother. For the majority of the first season, she is a distant character in Ricky's past. She has been to jail a few times due to drug possession and Ricky often felt bitter towards her because she failed to protect him from his father's abuse. But in Season 3, episode 7, she comes back into his life, to spend time with her son before she gets put back in jail. Ruben Enriquez (Adrian's father), as a DA helps Ricky get his mother out of jail, as he is willing to try and forgive her. Later on in the season, the two begin to repair the relationship, however, she was unsure about telling him she has a girlfriend, but she later does, and is gratified when Ricky seems pleased for her. The relationship doesn't last, though, and after a night of binge drinking (with the purported intent of convincing Ben that he shouldn't drink) she moves out of Margaret and Shakur's home and moves in with George Juergens, who initially tries to make a play for her, but remains pals when he discovers that she is a lesbian. She is very proud of Ricky's accomplishments in spite of his shaky childhood.

Allen Evangelista portrays Henry 'Hank' Miller, has been Ben's friend since the third grade. He is now dating Alison 'Alice' Valko (who is portrayed by Amy Rider), who has also become a friend of Ben's and some of the girls in school. Alice is very smart and knows a lot of factual information, while Henry is a bit more social. They have and discuss sex quite often, but fairly maturely. In the first episode, Alice pointed out Amy to Ben. In season 4 Henry breaks up with Alice and the two try "shared custody" of Ben, which is awkward and doesn't work out. In the 13th episode of Season 4, Alice walks into a bedroom after a graduation party to find Henry in bed with Adrian. Angrily, she tells Ben what she found, and Ben tells Henry he is no longer welcome in his home. After Ben finds out that he can no longer date Dylan, a sad conversation with Alice turns into sex. Henry thinks that there is something going on that he doesn't know about and pressures Alice to tell him. Ben doesn't know that Alice told Henry, and is mad at him for kissing Dylan.

Jorge Pallo portrays Marc Molina, who was the school guidance counselor and was a big hit with the girls at the start of the school year. Before Amy reveals her pregnancy to her two best friends, Lauren and Madison, they gab about the new counselor, asking if she has something better to talk about than him. He's always helping people, especially Ben and Adrian. He disappeared before the season break, with people saying that he ran off with Adrian, but no one really knew why he was gone. It was later revealed that he left to get married. We later find out that his wife was his crazy girlfriend that he talked about with Ben and also that he was once a cop until his wife made him quit the force. Marc believes he married the wrong person, but it is revealed that his wife is pregnant when she comes to Amy's baby shower. He eventually resigned because he needed a better job to support his growing family.

Alice Hirson portrays Mimsy, Anne's mother, Amy, Ashley and Robie's grandmother and John Juergens great-grandmother. She has the beginnings of Alzheimer's disease and recently moved to an assisted care home. It is stated that she likes everyone better than Anne, and Anne is reluctant to tell her about anything in her life, such as her marital problems with George as well as her pregnancy. Anne and Amy worry about her sometimes. Mimsy is reported as having suffered a slight stroke and therefore, Anne and George miss John's first birthday to go to her side. Mimsy surprises Anne and George with the news that she has married a gentleman named Eugene Levy. In season 5, Ashley takes advantage of her Alzheimer's and convinces Mimsy to give her $10,000 to run away to Italy for cooking school. Alice Hirson previously portrayed Jenny Jackson, mother of Annie Camden in 7th Heaven.

Josie Bissett, of Melrose Place fame, portrays Kathleen Bowman, who is the mother of Grace Bowman, adoptive mother of Tom Bowman, the ex-wife of George Juergens, and new wife of Jeff Tseguay. She cheated on George during their marriage. As a teen, Kathleen's mother did not let her have any physical contact with any boys. She told Grace that she only married George for sex. She waited until she married Marshall Bowman to have sex with him. She becomes a widow after Marshall dies in a private jet crash and began dating a younger man named Dr. Jeff Tseguay, a gynecologist, much to Grace's displeasure. Kathleen and Jeff are so excited that Grace suddenly seems to be in favor of the marriage that they impulsively decide to marry right away. Kathleen therefore changed her name from "Bowman" to "Tseguay". Kathleen tries to balance supervising Tom's special needs with his desire to be independent, and tries to get Grace to behave responsibly when it comes to sex. Kathleen then gets back together with George Juergens in a serious relationship.

Luke Zimmerman portrays Tom Bowman, Grace's adopted older brother, who has Down Syndrome. His mother died earlier in his life, then he was adopted by the Bowmans. With the normal drives of a young man, he is interested in sexâ€”at one point, he calls an "escort" service and a prostitute named Betty comes in response to his call. They do not have sex, but she spends the evening talking with him and allowing him to confess his frustrations. Later, he meets Tammy and wants to marry her, despite having only been on one date with her. Tammy ends up marrying someone else. He sometimes refers to Ricky as "Drummer Boy" and cares deeply about Grace. He mistakes Adrian's manipulation of him to borrow money as interest in him, and tries to respond, with no luck. When it is first announced that Adrian is pregnant, Tom proposes to her, and promises to take care of her. She gently refuses him. He and Jack share the Bowman's guesthouse for a while when Tom is impatient for more independence that Kathleen is willing to allow him. Jack moves into the main house when Tom begins dating a woman with two children that he met on the bus on his way to work as a Vice President of Human Resources.

John Schneider portrays Dr. Marshall Bowman, Grace's overprotective father. He's also the partner of the Juergens' pediatrician, Dr. Hightower, which is how he found out about Amy's pregnancy. Marshall later admits to Ricky that his brother was sexually abused by his neighbor and later committed suicide. Marshall dies when his private jet crashes, leaving Grace thinking the crash was all her fault because she had sex with her boyfriend, Jack, after Marshall told her not to. His body was cremated and spread on a hole in a golf course. It was discovered in Season 4, that Marshall had a relationship with another woman while he was in Zimbabwe and they had a son together named Jacob.

Renee Olstead portrays Madison Mildred Cooperstein. She is in 12th grade, she's one of Amy's best friends, and her values are defined by her Catholicism. Madison unintentionally spreads gossip and rumors, though she is a well-meaning girl. She dated Lauren's brother, Jason, and unintentionally spread the news of Amy's pregnancy. She feels ignored by Amy because she is spending more time with Ben than with her. Madison broke up with Jason but started to have feelings over the breakup. It is revealed that her mother died. Madison seems to have a crush on Jack and might have done something with him over the summer. She does not want a relationship with Jack despite fooling around with him. After Jack and Grace's relationship fizzles, Jack begins to date Madison. Madison, hoping to reassure Jack that she is a "free spirit" and doesn't want to trap him, tells Jack that she's not interested in children or marriage. This causes Jack to rethink the relationship because, as he tells her, the whole idea of dating is to find someone that you might want to marry. Since she says she doesn't want to marry, perhaps he should be dating elsewhere. Madison quickly recants and tells Jack that she is interested in a family and children, but not for a long time. They resume their relationship, and while Madison is seriously considering having sex with Jack, she confesses that she isn't quite ready, wanting the occasion to be special and wearing a pretty dress and having her make-up done. Jack tells her that he is fine with waiting. So, to get around having actual sex, Madison and Jack often have oral sex. After school ends, Madison sleeps over at the Bowman guest house (where Jack stays) and lies about where she spent the night. When her dad gets an email from Lauren, he forbids Madison and Jack to date. Madison later tries to date her former supervisor, whom her father discovers lied about his age, and proceeds to kick him out of his home. Madison lost her virginity to Jack after Adrian and Ben's wedding, but because she and Jack regret having sex, they decide to discontinue any sexual activity. At the graduation party Madison has sex with Lauren's boyfriend, Jesse. Lauren tells her that she hates her, orders her out of her house when Madison comes to apologize, and rips up a photo of the two of them. Lauren forgives her. Then they go to Berkeley because of their amazing singing voices. Then her and Jack get back together move to New York. They also get married. She becomes a great Broadway singer and Jack becomes a coach.

Camille Winbush portrays Lauren Treacy, who is also in the 12th grade and one of Amy's best friends. She is smart, practical, and seems to be the voice of reason for Amy. Her father is Ricky's therapist. Along with Madison, Lauren also accidentally spread the news of Amy's pregnancy. She made out with Ricky one night in his car. She also feels ignored by Amy. Her parents are divorced, and her mother is remarried. Lauren is now dating Jesse, and plans to have sex with him when Madison and Jack have sex. After her parents find out that she and Jesse slept over at Jack's guest house and she lied about it, her father and mother ban her from seeing and being with Jesse. She and Jesse break up, but then get back together when they realize they still care for each other. Jesse throws an all-night graduation party, where he drinks too much and ends up in bed with Madison after Lauren makes it clear that she neither intends to drink or have sex that night. Angrily, she breaks up with Jesse and tells Madison that she hates her. Camille Winbush also previously guest starred on 7th Heaven for 6 episodes as Lynn Hamilton.

Andrew McFarlane portrays Jason Treacy, Lauren's older brother and Madison Cooperstein's ex-boyfriend. He's a member of the Grant High Football team and portrayed as an excellent student, proven by the fact that he was the only other student besides Grace Bowman to be accepted into the Young Healers Camp program, for students who aspire to be doctors. At med camp, he and Grace became extremely attracted to one another because of all the time they spent together, and eventually they kissed. However, before returning home, they agreed to only be friends, but Jason still broke up with Madison before the next school year began. Along with Grace and her new boyfriend, Grant, he also attended the Young Healers Camp again the following summer.

Reid Scott portrays Dr. Jeff Tseguay, Grace's step-father. Jeff met Kathleen during the aftermath of Marshall's deathâ€”his brother died in the same plane crash that killed Marshall. Kathleen and Jeff's relationship is inadvertently discovered by Jack when he is in a drug store and witnesses Kathleen and Jeff purchasing contraceptives. He agrees not to tell Grace, but Kathleen decides to go ahead and tell Grace anyway, knowing that her interest in another man only six months after Marshall's death will deeply upset her. One evening, Kathleen is at Jeff's house and Jeff decides not to answer a phone call from his mother. His mother becomes concerned and bursts in on the couple talking in bed, much to Jeff's chagrin, Kathleen's embarrassment, and his mother's interest. Their relationship escalates quickly, and upon Grace's pretense at encouragement, they decide to marry. The day after the wedding, Jeff talks to Grace and tells her that he feels that they got off on the wrong foot, and, as her new stepfather and as an obstetrician/gynecologist, invites her to talk about her misgivings. During the talk, Grace begins to sort out her conflicted feelings about sex. Jeff later joins a medical team working for an extended period in Africa, where Grace visits him and meets Daniel. Jeff invites Kathleen to join him in Africa for a few months, and although tempted, she doesn't feel that she can leave Tom and Grace.

Jennifer Coolidge portrays Betty, who meets and interests Leo Boykewich. She is upfront about telling him that she has been a prostitute, because she doesn't want him embarrassed when he finds out, but he decides he doesn't care. He discovers that she can't marry him because she is still married to a man she hasn't seen in a long time. Leo locates her husband, only to find that he has died, and he proposes. When Ben is conflicted over having sex with Adrian, Betty offers to listen to his problems, but Ben rudely turns her away, telling her he doesn't need advice from a prostitute. She is hurt, but soon bounces back. When Ben sincerely apologizes for his outburst, she assures him that she has already forgotten it, and goes on to encourage Ben to act on his feelings. Betty and Leo are married in a lavish wedding with Ben inviting all his friends to celebrate. Betty clumsily but earnestly attempts to console Adrian after the loss their baby. In season 4 she decides that she realizes that Leo is not happy and tells him she wants a divorce and wants to go to college. In one of the last episodes of the season her mother dies and while awaiting a flight on her soon-to-be ex-husband's private jet she is approached by a divorce lawyer.

Bryan Callen portrays Robert "Bob" Underwood, Ricky's biological father who has been to jail for drugs and child molestation. In Season 1 during one episode he comes back to find Ricky, and wants to sell Ricky and Amy's baby. Later, he is caught with drugs and sent back to prison. Bryan Callen also previously guest starred on 7th Heaven for 9 episodes as George 'Vic' Vickery Petrowski.

L. Scott Caldwell portrays Margaret Shakur, Ricky's foster mother and John Juergens' foster grandmother. Margaret and her husband love Ricky as their own, and are proud to be his parents. Later, Margaret and Sanjay have dinner with Anne and George to discuss Ricky's custody case, and expressing a desire to be a part of John's life. Margaret helped Adrian with her decision about whether or not to terminate her unplanned pregnancy. Later, Ricky's birth mother, Nora, moves in with Margaret and Sanjay when starting her life over, and they have become good friends. Margaret decides to take in one of Ricky's former foster brothers, Ethan, who ends up in juvenile detention after sexting nude pictures of an underage girl to his friends when she breaks up with him. Because of overcrowding in juvenile detention, Ethan will return to live with Margaret.

Paola Turbay portrays Cindy Lee, Adrian's mother. Cindy got pregnant with Adrian as a teenager on purpose because she wanted the love of a baby, but her guilt of trapping Ruben Enriquez, Adrian's father, into being a father caused her to keep Ruben out of their lives. She raised Adrian alone and worked as a flight attendant; causing her to be away from home a lot. At the start of the show, she and George Jurgens had an affair that ended around the time George found out about Amy's pregnancy. She was also unaware of Adrian's affairs and her moniker as the "school slut" until Ruben told her. Despite this, Cindy continues to work, leaving Adrian alone, where Adrian continues to have sex. Cindy and Ruben later reunite after he leaves his wife, and she declines a job promotion in New York so they could get married. After a minor case of cold feet, Cindy and Ruben decide to get married the day before Leo and Betty's wedding in a judge's office. Much to Cindy's consternation, Ruben's mother has sent a completely inappropriate wedding dress to wear â€” an ugly red, flouncy dress several sizes too large. After a moment of anger, Cindy shrugs and she and Ruben are married, with Adrian as a witness. When Adrian reveals that she's pregnant, Cindy tells her daughter that she will stand behind Adrian, whether or not she decides to have an abortion. This spawns an argument between her and Ruben since he's Catholic. They later make up and support Adrian's decision to have the baby. Cindy and her husband are present for Adrian and Ben's wedding, and she later try's to comfort her daughter after the baby's stillbirth.

Philip Anthony-Rodriguez portrays Ruben Enriquez, Adrian's father and the ex-boyfriend of Cindy. He was not involved with Adrian during her childhood years because he and Cindy made a deal not to see each other. When Adrian eventually finds him, Ruben tells Adrian he wants nothing do with her, but later decides to help her turn her life around for the better. Ruben is an Assistant District Attorney and is married for the third time. Adrian is his second biological child (he has a biological son in Mexico), however, he is the stepfather to two sons. For confidentiality reasons, he could not tell Adrian that he had known the truth about Ricky having been sexually abused. He and Cindy marry before a judge, "Fast Eddy", the day before Leo and Betty marry. When his daughter becomes pregnant, Ruben strongly objects to the idea of her having an abortion. This causes conflict between Ruben and his wife, who supports Adrian's decision. Adrian chose to keep the baby, and Ruben couldn't have been happier. When Adrian's daughter, later named "Mercy" is born stillborn, he blames himself for pushing Adrian to keep the baby instead of having an abortion.

Tom Virtue portrays Rev. Sam Stone, Jack's stepfather and the minister at the local church. Jack told him why Grace thinks her dad died. He tried, unsuccessfully, to make Grace see that she and Jack having sex had nothing to with her father's death. He also helped Amy find couples to adopt her unborn baby (John) when she was pregnant. After offered a job at his Alma Mater in Phoenix, Arizona as the head of the Philosophy department, he gives up the church and moves with his wife, leaving Jack to complete his senior year. He makes a cameo appearance to marry Ben and Adrian.

Brando Eaton portrays Griffin, who is in 9th grade like Ashley, and is her friend. He and Ashley clicked as friends when he asked her to sit with him at lunch. After she asks him if all he wants is to have sex with her, Griffin tells Ashley that he is gay. George likes Griffin after meeting him because Ashley did not pick a guy friend who only wants her for sex. It's revealed that his two older brothers are also gay. He fixes Ashley up with his cousin, Grant, and brings his date, Michael, to Leo and Betty's wedding. After Ashley uses Grant, Griffin decides to introduce him to Grace Bowman. In return, Grace introduces Griffin to Peter, a guy she knew from church, and it was an instant connection for both couples.

Beverley Mitchell portrays Katelyn O'Malley. Mitchell is the third person from the show that previously starred on 7th Heaven; Mackenzie Rosman was the second, playing a recurring role as Zoe and Christopher Michael was the first, playing the football coach. Katelyn is the most recent school guidance counselor. It is revealed in season 4 that like Ben and Adrian, she lost a child when her baby died of SIDS. She also explains that her marriage fell apart as well when her husband became an alcoholic.

Dylan is introduced during the graduation party. Henry points her out and Ben goes after her. Dylan's parents are very protective over her and it takes a while for them to be convinced that it is okay for them to date. Ben's dad and Dylan's parents catch Dylan and her friends smoking pot in Ben's room. They are then forbidden to see each other. After some convincing they are allowed to go out again but they accidentally burn down Dylan's school, and they are forbidden to see each other again. Even though her friend, Wendy, told her that she overheard Ben telling Amy that he still loves her, she still wants to date Ben. They come up with this idea that her parents could meet Henry and pretend to go out with Henry, but instead meet Ben. Ben's dad finds out and forbids him from going. At her house, Henry is mad at Ben for sleeping with Alice and plans to make revenge by going out with Dylan for real. So he forces her to stay home and have a real date. Dylan is furious with Henry, but they still kiss. Dylan then finds out that Ben and Alice slept together and doesn't really want to go out with Ben anymore so she gives Henry a chance. She is portrayed by Ana Lucasey.

Austin Stowell portrays Jesse. He became Lauren's boyfriend in season 2. After sleeping at Jack's guest room with Madison and Lauren, Lauren is banned from seeing Jesse. At his graduation party, where he drinks too much, Lauren discovers him sleeping with Madison.

Kathy is portrayed by Cierra Ramirez, introduced in the 100th episode as a new freshman who Amy mentors as part of a senior project. She got pregnant by her much older ex-boyfriend, and plans on giving her baby girl up for adoption. She is initially wary about talking to Amy because unlike her, she chose to raise a child as a teenager. Kathy eventually opens up to her about her worries on not having friends because of her condition. She currently lives with her grandmother because her parents kicked her out. Kathy explains early on that even though her baby will have an open adoption, she has no plans to be involved in the child's life. She meets Ethan and they start connecting about their histories and even go on a double-date with Amy and Ricky. Their relationship hits a speed bump in the road after Ethan makes a disastrous first impression to the prospective parents, who later tell Kathy to break-up with him. They quickly get back together in the fall season finale. In the holiday special, Kathy goes into labor on Christmas Eve and gives birth to a baby girl on Christmas Day. The adoptive parents name her Hedy. She is portrayed by Cierra Ramirez.

Played by Michael Grant, Ethan is Ricky's 14-year-old foster brother who ran away from their house a few years after stealing a knife from Margaret and Shaker. He first appears when he gets into trouble for sending naked pictures of his ex-girlfriend to everyone in his contacts, which ultimately lands him in juvenile detention. Margaret decides to take him in again, and forces him to go back to school. In season 4 he is forced to go to summer school and immediately gets into trouble for stealing condoms from the nurse's office. Despite his actions, Ricky still tries to install sense in him remembering his early days before he met Amy. He begins dating Kathy, who is pregnant with her ex-boyfriend's child. They decide to take their relationship slow, but Ethan has trouble respecting Kathy's boundaries. Such as when he meets the perspective parent's of Kathy's unborn daughter, and asks rude and personal questions about them. Kathy breaks up with him when her perspective parent's think he is too unstable to be around. Ethan later confides to Kathy that his biological father injured him when he was a kid, causing his distrust in adults. After meeting Kathy, Ethan tries several times to get advice from Ben on how to be a good boyfriend to someone who is having a child with another guy, but Ben show's no interest in helping him. In the episode "Holly Rollers", he is shown to be a talented piano player. Then him and Amy start getting closer and closer while Amy and Ricky get farther.

The following is a list of characters that appear on the show, but usually do not add to the overall plot or story line of the series.

Constance Marie portrays Mrs. Virginia Molina, Mr. Molina's new wife. They are expecting a baby around the same time as Amy. She shows up at Amy's baby shower after being invited by Joe.

Amy and Ricky's now three-year-old son whom they conceived on a night at band camp when Amy was a freshman and when Ricky was a sophomore in high school. Ashley (Amy's sister) is the one who suggested John's name because "his life was going to be complicated already, so we might as well give him an easy name." His birthday is 06/06/09. His parents Amy and Ricky break apart from their marriage plans and Amy goes to college, leaving Ricky as a single father.

Kristin Bauer van Straten portrays Mrs. Stone, Jack's mother. She met her second husband at grief counseling. Her voice is heard once yelling at Jack when he throws a football into the window. She and her husband tell Jack about his new job in Arizona, requiring Jack to find a new place to live to prevent him from relocating during his senior year. And at one of the last episodes of 2012 she shows up at the last few minutes of the show to pray while Jack lies in his hospital room comotized he comes back after jack gets into coma

Kristopher Higgins portrays Peter, who is introduced in the Season 3 episode "Chicken Little". Peter becomes a love interest for Griffin when Grace sets them up believing Peter is gay. After talking with both his father and Griffin, Peter comes out as gay, and pursues a relationship with Griffin.

Katelyn Tarver portrays Mercedes, who is one of the friends of Dylan, Raven, and Wendy. Her first appearance was in Smokin' Like a Virgin, although she was probably at Dylan's party (before everyone ended up at the cabin next door, where Jesse and everyone else from the main cast was). She went over to Ben's house with Dylan and she smoked pot because she was depressed after her mom died and her mom had a prescription.


how fast would nascar cars go without restrictor plates

Rusty Wallace tested a car at Talladega Superspeedway without a restrictor plate in 2004, reaching a top speed of 228 mph (367 km/h) in the backstretch and a one-lap average of 221 mph (356 km/h).[5] While admitting excitement at the achievement, Wallace also conceded, "There's no way we could be out there racing at those speeds... it would be insane to think we could have a pack of cars out there doing that."[5]

Restrictor plate

A restrictor plate or air restrictor is a device installed at the intake of an engine to limit its power. This kind of system is occasionally used in road vehicles (e.g., motorcycles) for insurance purposes, but mainly in automobile racing, to limit top speed to provide equal level of competition, and to lower costs; insurance purposes have also factored in for motorsports.

A few top classes like Formula One limit only the displacement and air intake mouth dimension. However, in 2006 air restrictors (as well as rev limiters) were used by Scuderia Toro Rosso to facilitate the transition to a new engine formula.

Many other racing series use additional air restrictors.

After Group B cars were outlawed from rallying because they were too powerful (rumored to have reached 600 hp), too fast and too dangerous, the FISA decided that rally cars should not have more than 300 hp (220 kW). For a while no special restrictions were needed for that (e.g. the Group A Lancia Delta HF 4WD had about 250 hp in 1987). But with development in the 1990s, Group A cars were rumored to have reached 405 hp or more. So the FIA mandated restrictors for supercharged and turbocharged engines in all categories (World Rally Car, Group A and Group N).

This means that the rally version of a car like the Mitsubishi Lancer Evolution can have less power than the street version (the "280" hp Evo VII was believed to have more than 300Â hp, and in some markets the FQ-320, FQ-340, FQ-360, FQ-400 versions were sold, with the number representing the total horsepower).

It also means that the torque and power curves of the engine are unusual. The engine produces peak torque and almost maximum power at a relatively low RPM, and from there to the rev limiter the torque drops and the power does not increase much.

In 1995 Toyota Team Europe used an illegal device to bypass the restrictor (allowing an estimated extra 50Â hp). Due to this the team lost their results in the 1995 season and was banned from rallying until the end of 1996.

NASCAR's Monster Energy NASCAR Cup Series and Xfinity Series have used restrictor plates at Daytona International Speedway and Talladega Superspeedway since 1988. They are still in use with the 2012 season introduction of McLaren Electronics engine control unit providing electronic engine management for all NASCAR races and cars with carburetors finally being phased out.

The device limits the power output of the motor, hence slowing both the acceleration and the overall top speed obtainable on the tracks where the cars are so equipped. NASCAR routinely stated that the Monster Energy Cup restrictor plate reduces engine power from approximately 750 hp to approximately 430 hp.[citation needed]

A major effect, however, is that all drivers tend to form very large "packs" of cars that run closely together for the majority of the race. In these packs drivers often run three abreast across the track, consequently there may be as little as one second separating the entire field. These large packs reduce air resistance which allows the cars to run faster and makes drafting easier.

The restrictions are in the interest of driver and fan safety because higher speeds are closer to out-of-control than the 190 MPH range used for Daytona and Talladega; the severity of crashes at higher speeds is also much greater, shown by telemetry readings of wrecks such as Jerry Nadeau at Richmond and Michael McDowell at Texas that were far higher than registered on restrictor plate tracks. Drivers such as Rusty Wallace have also cited data showing that the sport's roof flaps cannot keep cars on the ground above 204 MPH.

At Daytona and Talladega, most races are marred by at least one multi-car crash as cars rarely become separated. Talladega has been considered the more likely track for these instances to occur as the track is wide enough to have three to four distinct lines of racing. With the new pavement at Daytona, three-wide racing is now possible and multi-car wrecks could become more common. The 2011 Daytona 500 saw a record number of cautions including an early 17-car pile-up. These wrecks tend to be singled out for criticism despite multicar crashes at other tracks and the generally greater severity of impact on non-restricted tracks. In addition, the packs were far smaller in 1988 through 1990 until more teams mastered the nuances of this kind of racing and improved their cars (and drivers) accordingly.

The 2011 Sprint Cup season was the last complete Cup season with carbureted engines. NASCAR announced that it would change to fuel injection for the 2012 season.[2] The injection system used by NASCAR is a different system from that used in IndyCar Racing and other motorsports series and restrictor plates are usable with the NASCAR system; they were used for January 2012 testing at Daytona. The current restrictor plates are bolted beneath a throttle body that sits in the same place as the former carburetors.[3]

There have been three reasons that NASCAR used restrictor plates.[citation needed]

The first use came in 1970 in response to escalating speeds. Following testing and input from drivers such as David Pearson, Bobby Isaac, and Bobby Allison, NASCAR mandated the use of a restrictor plate. Smaller engines, in the 358 cubic inch range, were exempt from the plates; the first car to race with a small block engine was Dick Brooks at the 1971 Daytona 500, where he ran a 1969 Dodge Daytona with a 305 CID engine. The transition period lasted until 1974, when the current 358 cubic inch (5870cc) limit was imposed and NASCAR eliminated the 427 cubic inch (7000cc) engine. As the early 1970s use of restrictor plates was considered a transitional process, and as not every car used restrictor plates, this is not what most fans call "restrictor plate racing."[citation needed]

The second use came following the crash of Bobby Allison at the 1987 Winston 500 at Talladega Superspeedway. Allison's Buick LeSabre blew a tire going into the tri-oval at 200 mph (320 km/h), spun around and became airborne, flying tail-first into the catch fencing.[4] While the car did not enter the grandstands it tore down nearly 100 feet of fencing and flying debris injured several spectators. After a summer where the two subsequent superspeedway races were run with smaller carburetors (390 cubic feet per minute (cfm) instead of 830 cfm) proved to be inadequate to sufficiently slow the cars, NASCAR imposed restrictor plates again, this time at the two fastest circuits, both superspeedways: Daytona for all NASCAR-sanctioned races and Talladega for Cup races. The Automobile Racing Club of America also enforced restrictor plates at their events at the two tracks. In 1992, when the Busch Grand National series began racing at Talladega, the plates were implemented, in keeping with their use at Daytona.[citation needed]

NASCAR's concerns with speeds because of power-to-weight ratios result in restrictor plates at other tracks. The Goody's Dash Series (known now as the ISCARS series with its new ownership) used restrictor plates at Bristol during at least the last years of the series' existence when the cars were using six-cylinder engines (compared to the traditional four cylinder engines), in addition to their Daytona races.[citation needed]

However, restrictor plates initially were not used for Camping World Truck Series trucks. Rather, aerodynamic, air intake reduction through the use of a 390 cfm carburetor, and eventually a tapered carburetor spacer were implemented for those races. Combined with the aerodynamic disadvantage of the trucks, this allowed NASCAR to avoid the use of such equipment for the trucks until 2008.[citation needed] In 2008, the Nationwide Series (now known as Xfinity Series) and Truck Series began implementation of tapered spacers in the engines to restrict power compared to Sprint Cup cars at all 35 (NNS) and 25 (NCTS) races. Both these NASCAR series now use a restrictor plate and tapered spacer at the two tracks.

The third use came in 2000. Following fatal crashes of Adam Petty and Kenny Irwin, Jr. at the New Hampshire International Speedway during the May Busch Series and July Winston Cup Series races, respectively, NASCAR adopted a one-inch (2.54 cm) restrictor plate to slow the cars headed towards the tight turns as part of a series of reforms to alleviate stuck throttle problems which were alleged to have caused both fatal crashes. For the Winston Cup race, it was used just once at the 2000 Dura Lube 300. Jeff Burton led all 300 laps in the ensuing race, despite a 23-car two-abreast battle in the first ten laps, a dramatic charge past 22 cars in 100 laps by John Andretti (who finished seventh), and two charges by Bobby Labonte in the final 50 laps where he took the lead but Burton beat him back to the stripe. The use of restrictor plates, intended as an emergency measure pending a more permanent replacement in any event, was discontinued at New Hampshire for the following race for Cup only. However, the Modifieds still use a restrictor plate because the speeds are too great for that class of racecar without them. The track has since been changed with soft walls to improve racing safety.[citation needed] Restrictor plates remain a permanent fixture to the Modifieds and the racing has often broken 20 official lead changes for 100–125 laps of competition.

A frequent criticism of restrictor plates is the enormousness of packs in the racing, with "Big One" wrecks as noted above singled out for condemnation despite the greater violence of "smaller" crashes on unrestricted tracks. In restrictor plate racing the packs have brought about an often-enormous increase in positional passing; at Talladega Superspeedway the Sprint Cup cars have broken 40 official lead changes sixteen times from 1988 onward, including both 2010 Sprint Cup races at Talladega, which had 87 official lead changes in the regulation 188 laps. (The 2010 Aaron's 499 had 88 lead changes, but the 88th – the race-winning pass by Kevin Harvick – was on the last lap of the third attempt at a green-white-checkered finish). Daytona International Speedway has generally been less competitive because the age of the asphalt (the track was repaved in 1978 and again in 2010) has reduced grip for the cars and thus handling has impeded passing ability to a significant extent. The 2000 New Hampshire race was condemned because Jeff Burton led wire to wire; the plates were singled out as impeding ability to pass, a criticism contradicted by the use of restrictor plates in a Busch North support race the day before where the lead changed seven times in 100 laps and by the highly competitive nature of restrictor plated Modified races; as noted above the 300 also saw a 23-car battle for third in the first ten laps and a burst by 22 cars from John Andretti.

The criticism stems from reduction in throttle response brought by the restriction. The reduction in throttle response, however, has never been shown to have impeded ability to pass; the criticism was shot down in the first "modern" plate race, the 1988 Daytona 500, as the lead changed 25 times officially and saw several bursts where the lead changed several times a lap and also several bursts of sustained side-by-side racing, notably in the final 50 laps between Bobby Allison, Darrell Waltrip, Neil Bonnett, and Buddy Baker.

Said Waltrip before the race, "I feel, as a driver, now I can do more than I could before (the plates). Now, instead of a car just blasting by me with a burst of speed and a lot of horsepower, he's got to think his way, he got to DRIVE his way around me."

In the transitional years (1971â€“74) where the seven-litre engines (427ci) had restrictor plates, Daytona and Talladega broke 40 official lead changes six times, while Michigan International Speedway broke 35 official lead changes in both of its 1971 races.


who was governor of virginia when british forces burned richmond

Prior to the beginning of the raid, Thomas Jefferson, the then-Governor of Virginia, had moved the capital of Virginia from Williamsburg to Richmond, because of its strategically central, defensible location. In the event of an attack, Jefferson moved all of the town's military supplies to a foundry five miles outside of Richmond. Little did Jefferson know how big of an attack would soon follow.

Raid on Richmond

Sir Henry Clinton

The Raid on Richmond was a series of British military actions against the capital of Virginia, Richmond, and the surrounding area, during the American Revolutionary War. Led by American turncoat Benedict Arnold, the Richmond Campaign is considered one of his greatest successes while serving under the British Army, and one of the most notorious actions that Arnold ever performed.

Clinton hoped that sending an American-born commander to Richmond would convince more Loyalists in the area to join the British cause, which would subsequently give the British Army the upper hand in the Southern Theatre of the war.[1]

From the 1st to the 3rd of January, Arnold's fleet sailed up the James River, laying waste to plantations and settlements along the way. On the 4th of January, the British reached their destination, Westover Plantation, where they would ready themselves for the assault against Richmond. In the afternoon, Arnold and his men disembarked on foot towards Richmond.

The following day, Arnold's force of Loyalist "green-coats", consisting of infantry, dragoons, and artillery, arrived at Richmond, which was defended by about 200 militiamen. Surprisingly enough, most Virginia militiamen had not bothered to defend their capital because they had already served their time in battle, and thought that their duty was up. Upon seeing the group of Virginia militiamen, Colonel John Graves Simcoe, of the Queen's Rangers, ordered a detachment of soldiers to confront them. The militiamen fired a weak musket volley at the advancing British, and then broke and ran into the woods, with the Loyalist detachment chasing after them. Jefferson, seeing his militiamen dispersed, and no other plausible way to defend Richmond, quickly ordered the mass-evacuation of most military supplies from the city, and promptly fled in his carriage, along with the rest of Virginia's government officials and his family.

At noon, Arnold's forces marched triumphantly into the city, described by an eyewitness as "undisturbed by even a single shot." From his headquarters at Main Street's City Tavern (he would only stay in Richmond for a day), Arnold wrote a letter to Jefferson, saying that if he could move the city's tobacco stores and military arms to his ships, he would leave Richmond unharmed. Jefferson's response was livid, refusing that a turncoat do anything to Richmond's supplies.[2]

Upon receiving the letter the next day on January 6, Arnold was enraged, and ordered Richmond to be set to the torch. British troops then started a rampage across the city, burning government buildings as well as private homes, ransacking the city of its valuables and supplies. A strong wind spread the flames even more, adding to the destruction. After most of Richmond was burned and its valuables sacked, Arnold led his forces outside of Richmond and to the Westham cannon foundry, which held even more armaments, and preceded to burn it down. After its destruction, the British went down to the city of Chesterfield, and began another spree of violence, burning down homes and looting buildings.

When the news of Richmond's destruction reached Jefferson, he was aghast. Arnold's British force had entered Virginia's very capital, unopposed, and had singlehandedly defiled it. The Governor called his friend, Sampson Mathews, the Colonel of the Virginia militia, and ordered him to assault Arnold's forces. Mathews built up a group of around 200 militiamen, and embarked hastily to catch and damage Arnold's slow-moving army near Richmond.

Eventually, delayed by bad weather, sickness and mutiny, Mathews' forces caught up with Arnold's army, and attacked it by surprise. Using nimble tactics popularized by American commander Nathanael Greene, the militiamen managed to inflict significant casualties on Arnold's army, and over the following days, the British ranks were thinned by multiple skirmishes around Richmond and the James River. Eventually, Arnold considered the skirmishes between his American Legion and the Patriots to be so serious, that he ordered his army to retreat to Portsmouth, in order to set up defensive fortifications there and wait for reinforcements.

Thus, the British army moved quickly down the James River, burning more plantations and homes in their wake, while still being chased by Mathews. One of the plantations that Arnold's men burned on their retreat was that of Berkeley Plantation, the home of Founding Father Benjamin Harrison V. Harrison was going about his regular duties in his mansion, when he saw the British force advancing towards his plantation. He quickly informed his wife and children, and they then escaped in a carriage. Arnold knew that Berkeley belonged to Harrison, whom he viewed as a traitor, and wanted to punish him for treason against Great Britain. All of the Harrison family's portraits and artwork were taken outside and 40 of Harrison's slaves were confiscated. Arnold spared Harrison's mansion and houses, however, as he believed the war would soon be won by the British, and desired a grand plantation in which to live after the war. The only original portrait of Harrison to survive was the miniature around his wife's neck, wearing it as she fled from the British forces.

On January 19, the Richmond Campaign ended, when Benedict Arnold's weary troops reached Portsmouth. They had survived a great ordeal, and Arnold was praised by local Loyalists, as well as his superiors, to be a hero. On the same day, General William Phillips arrived to relieve Arnold with 2,000 fresh troops, and to assume command over Portsmouth's defenses. Even though days of turmoil had ended, they would live on as some of Benedict Arnold's finest hours.

The destruction of Richmond, one of the most important cities in the United States, outraged the American populace. George Washington was so angered and humiliated by the destruction of Richmond, that he put a 5,000 guinea bounty on Arnold's head and ordered his aide, the Marquis de Lafayette, to hang Arnold if he encountered him in battle. Continental marksmen were issued targets painted in Benedict's appearance to practice on, if in the event they saw him.

The British, on the other hand saw Arnold's victory at Richmond as a turning point, and gave them hopes that Loyalists could rise up with them, and quell the American presence in the South. Many slaves were liberated from the raided plantations, as well as Richmond itself, and many of them promptly joined the British Army afterwards, in exchange for their freedom. After Arnold's initial raid on the James River and the area around Richmond, more minor raids ensued. British commanders like William Phillips and Banastre Tarleton followed in Arnold's example, raiding and burning more outlying towns and preying on Continental troops. Benedict Arnold, the Continental Army's brilliant General, had guaranteed himself a place in the British ranks with the Richmond Campaign, as well as a spot in the annals of history.


what is z transform in digital signal processing

The Z-transform can be defined as either a one-sided or two-sided transform.[7]

Z-transform

In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.

It can be considered as a discrete-time equivalent of the Laplace transform. This similarity is explored in the theory of time scale calculus.

The basic idea now known as the Z-transform was known to Laplace, and it was re-introduced in 1947 by W. Hurewicz[1] and others as a way to treat sampled-data control systems used with radar. It gives a tractable way to solve linear, constant-coefficient difference equations. It was later dubbed "the z-transform" by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952.[2][3]

The modified or advanced Z-transform was later developed and popularized by E. I. Jury.[4][5]

The idea contained within the Z-transform is also known in mathematical literature as the method of generating functions which can be traced back as early as 1730 when it was introduced by de Moivre in conjunction with probability theory.[6] From a mathematical view the Z-transform can also be viewed as a Laurent series where one views the sequence of numbers under consideration as the (Laurent) expansion of an analytic function.

The bilateral or two-sided Z-transform of a discrete-time signal x[n] is the formal power series X(z) defined as

where n is an integer and z is, in general, a complex number:

where A is the magnitude of z, j is the imaginary unit, and É¸ is the complex argument (also referred to as angle or phase) in radians.

Alternatively, in cases where x[n] is defined only for n â‰¥ 0, the single-sided or unilateral Z-transform is defined as

In signal processing, this definition can be used to evaluate the Z-transform of the unit impulse response of a discrete-time causal system.

An important example of the unilateral Z-transform is the probability-generating function, where the component x[n] is the probability that a discrete random variable takes the value n, and the function X(z) is usually written as X(s), in terms of s = zâˆ’1. The properties of Z-transforms (below) have useful interpretations in the context of probability theory.

In geophysics, the usual definition for the Z-transform is a power series in z as opposed to zâˆ’1. This convention is used, for example, by Robinson and Treitel[8] and by Kanasewich.[9] The geophysical definition is:

The two definitions are equivalent; however, the difference results in a number of changes. For example, the location of zeros and poles move from inside the unit circle using one definition, to outside the unit circle using the other definition.[8][9] Thus, care is required to note which definition is being used by a particular author.

The inverse Z-transform is

where C is a counterclockwise closed path encircling the origin and entirely in the region of convergence (ROC). In the case where the ROC is causal (see Example 2), this means the path C must encircle all of the poles of X(z).

A special case of this contour integral occurs when C is the unit circle. This contour can be used when the ROC includes the unit circle, which is always guaranteed when X(z) is stable, that is, when all the poles are inside the unit circle. With this contour, the inverse Z-transform simplifies to the inverse discrete-time Fourier transform, or Fourier series, of the periodic values of the Z-transform around the unit circle:

The Z-transform with a finite range of n and a finite number of uniformly spaced z values can be computed efficiently via Bluestein's FFT algorithm. The discrete-time Fourier transform (DTFT)—not to be confused with the discrete Fourier transform (DFT)—is a special case of such a Z-transform obtained by restricting z to lie on the unit circle.

The region of convergence (ROC) is the set of points in the complex plane for which the Z-transform summation converges.

Let x[n] = (0.5)n. Expanding x[n] on the interval (−∞, ∞) it becomes

Looking at the sum

Therefore, there are no values of z that satisfy this condition.

Let

x
[
n
]
=

0.5

n

u
[
n
]

{\displaystyle x[n]=0.5^{n}u[n]\ }

 (where u is the Heaviside step function). Expanding x[n] on the interval (−∞, ∞) it becomes

Looking at the sum

The last equality arises from the infinite geometric series and the equality only holds if |0.5zâˆ’1| < 1 which can be rewritten in terms of z as |z| > 0.5. Thus, the ROC is |z| > 0.5. In this case the ROC is the complex plane with a disc of radius 0.5 at the origin "punched out".

Let

x
[
n
]
=
−
(
0.5

)

n

u
[
−
n
−
1
]

{\displaystyle x[n]=-(0.5)^{n}u[-n-1]\ }

 (where u is the Heaviside step function). Expanding x[n] on the interval (−∞, ∞) it becomes

Looking at the sum

Using the infinite geometric series, again, the equality only holds if |0.5âˆ’1z| < 1 which can be rewritten in terms of z as |z| < 0.5. Thus, the ROC is |z| < 0.5. In this case the ROC is a disc centered at the origin and of radius 0.5.

What differentiates this example from the previous example is only the ROC. This is intentional to demonstrate that the transform result alone is insufficient.

Examples 2 & 3 clearly show that the Z-transform X(z) of x[n] is unique when and only when specifying the ROC. Creating the pole–zero plot for the causal and anticausal case show that the ROC for either case does not include the pole that is at 0.5. This extends to cases with multiple poles: the ROC will never contain poles.

In example 2, the causal system yields an ROC that includes |z| = âˆž while the anticausal system in example 3 yields an ROC that includes |z| = 0.

In systems with multiple poles it is possible to have an ROC that includes neither |z| = âˆž nor |z| = 0. The ROC creates a circular band. For example,

has poles at 0.5 and 0.75. The ROC will be 0.5 < |z| < 0.75, which includes neither the origin nor infinity. Such a system is called a mixed-causality system as it contains a causal term (0.5)nu[n] and an anticausal term −(0.75)nu[−n−1].

The stability of a system can also be determined by knowing the ROC alone. If the ROC contains the unit circle (i.e., |z| = 1) then the system is stable. In the above systems the causal system (Example 2) is stable because |z| > 0.5 contains the unit circle.

If you are provided a Z-transform of a system without an ROC (i.e., an ambiguous x[n]) you can determine a unique x[n] provided you desire the following:

If you need stability then the ROC must contain the unit circle. If you need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. If you need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence. If you need both, stability and causality, all the poles of the system function must be inside the unit circle.

The unique x[n] can then be found.

with

K

Z

:=
{
K
r
:
r
∈

Z

}

{\displaystyle K\mathbb {Z} :=\{Kr:r\in \mathbb {Z} \}}

the z-domain

ROC possibly excluding the boundary, if

X
(
z
)

{\displaystyle X(z)}

 is irrational[10]

Parseval's theorem

Initial value theorem: If x[n] is causal, then

Final value theorem: If the poles of (zâˆ’1)X(z) are inside the unit circle, then

is the unit (or Heaviside) step function and

is the discrete-time unit impulse function (cf Dirac delta function which is a continuous-time version). The two functions are chosen together so that the unit step function is the accumulation (running total) of the unit impulse function.

For values of z in the region |z|=1, known as the unit circle, we can express the transform as a function of a single, real variable, ω, by defining z=ejω.  And the bi-lateral transform reduces to a Fourier series:

∑

n
=
−
∞

∞

x
[
n
]

z

−
n

=

∑

n
=
−
∞

∞

x
[
n
]

e

−
j
ω
n

,

{\displaystyle \sum _{n=-\infty }^{\infty }x[n]\ z^{-n}=\sum _{n=-\infty }^{\infty }x[n]\ e^{-j\omega n},}

which is also known as the discrete-time Fourier transform (DTFT) of the x[n] sequence. This 2Ï€-periodic function is the periodic summation of a Fourier transform, which makes it a widely used analysis tool. To understand this, let X(f) be the Fourier transform of any function, x(t), whose samples at some interval, T, equal the x[n] sequence. Then the DTFT of the x[n] sequence can be written as:

∑

n
=
−
∞

∞

x
(
n
T
)

⏞

x
[
n
]

e

−
j
2
π
f
n
T

⏟

DTFT

=

1
T

∑

k
=
−
∞

∞

X
(
f
−
k

/

T
)
.

{\displaystyle \underbrace {\sum _{n=-\infty }^{\infty }\overbrace {x(nT)} ^{x[n]}\ e^{-j2\pi fnT}} _{\text{DTFT}}={\frac {1}{T}}\sum _{k=-\infty }^{\infty }X(f-k/T).}

When T has units of seconds,

f

{\displaystyle \scriptstyle f}

 has units of hertz. Comparison of the two series reveals that

ω
=
2
π
f
T

{\displaystyle \scriptstyle \omega =2\pi fT}

  is a normalized frequency with units of radians per sample. The value ω=2π corresponds to

f
=

1
T

{\displaystyle \scriptstyle f={\frac {1}{T}}}

 Hz.  And now, with the substitution

f
=

ω

2
π
T

,

{\displaystyle \scriptstyle f={\frac {\omega }{2\pi T}},}

  Eq.1 can be expressed in terms of the Fourier transform, X(•):

When sequence x(nT) represents the impulse response of an LTI system, these functions are also known as its frequency response. When the x(nT) sequence is periodic, its DTFT is divergent at one or more harmonic frequencies, and zero at all other frequencies. This is often represented by the use of amplitude-variant Dirac delta functions at the harmonic frequencies. Due to periodicity, there are only a finite number of unique amplitudes, which are readily computed by the much simpler discrete Fourier transform (DFT).Â  (See DTFT; periodic data.)

The bilinear transform can be used to convert continuous-time filters (represented in the Laplace domain) into discrete-time filters (represented in the Z-domain), and vice versa. The following substitution is used:

to convert some function

H
(
s
)

{\displaystyle H(s)}

 in the Laplace domain to a function

H
(
z
)

{\displaystyle H(z)}

 in the Z-domain (Tustin transformation), or

from the Z-domain to the Laplace domain. Through the bilinear transformation, the complex s-plane (of the Laplace transform) is mapped to the complex z-plane (of the z-transform). While this mapping is (necessarily) nonlinear, it is useful in that it maps the entire jΩ axis of the s-plane onto the unit circle in the z-plane. As such, the Fourier transform (which is the Laplace transform evaluated on the jΩ axis) becomes the discrete-time Fourier transform. This assumes that the Fourier transform exists; i.e., that the jΩ axis is in the region of convergence of the Laplace transform.

Given a one-sided Z-transform, X(z), of a time-sampled function, the corresponding starred transform produces a Laplace transform and restores the dependence on sampling parameter, T:

The inverse Laplace transform is a mathematical abstraction known as an impulse-sampled function.

The linear constant-coefficient difference (LCCD) equation is a representation for a linear system based on the autoregressive moving-average equation.

Both sides of the above equation can be divided by α0, if it is not zero, normalizing α0 = 1 and the LCCD equation can be written

This form of the LCCD equation is favorable to make it more explicit that the "current" output y[n] is a function of past outputs y[n−p], current input x[n], and previous inputs x[n−q].

Taking the Z-transform of the above equation (using linearity and time-shifting laws) yields

and rearranging results in

From the fundamental theorem of algebra the numerator has M roots (corresponding to zeros of H) and the denominator has N roots (corresponding to poles). Rewriting the transfer function in terms of poles and zeros

where qk is the k-th zero and pk is the k-th pole. The zeros and poles are commonly complex and when plotted on the complex plane (z-plane) it is called the pole–zero plot.

In addition, there may also exist zeros and poles at z = 0 and z = âˆž. If we take these poles and zeros as well as multiple-order zeros and poles into consideration, the number of zeros and poles are always equal.

By factoring the denominator, partial fraction decomposition can be used, which can then be transformed back to the time domain. Doing so would result in the impulse response and the linear constant coefficient difference equation of the system.

If such a system H(z) is driven by a signal X(z) then the output is Y(z) = H(z)X(z). By performing partial fraction decomposition on Y(z) and then taking the inverse Z-transform the output y[n] can be found. In practice, it is often useful to fractionally decompose

Y
(
z
)

z

{\displaystyle {\frac {Y(z)}{z}}}

 before multiplying that quantity by z to generate a form of Y(z) which has terms with easily computable inverse Z-transforms.