Differential Equation Essay Example for Free

Differential Equation Essay Assume that the resulting system is linear and time-invariant. x[n] O + r0n] D y[n] +1 3 -2 Figure P6. 5 (a) Find the direct form I realization of the difference equation. (b) Find the difference equation described by the direct form I realization. (c) Consider the intermediate signal r[n] in Figure P6. 5. (i) Find the relation between r[n] and y[n]. (ii) Find the relation between r[n] and x[n]. (iii) Using your answers to parts (i) and (ii), verify that the relation between y[n] and x[n] in the direct form II realization is the same as your answer to part (b). Systems Represented by Differential and Difference Equations / Problems P6-3 P6. 6 Consider the following differential equation governing an LTI system. dx(t) dytt) dt + ay(t) = b di + cx(t) dt dt (P6. 6-1) (a) Draw the direct form I realization of eq. (P6. 6-1). (b) Draw the direct form II realization of eq. (P6. 6-1). Optional Problems P6. 7 Consider the block diagram in Figure P6. 7. The system is causal and is initially at rest. r [n] x [n] + D y [n] -4 Figure P6. 7 (a) Find the difference equation relating x[n] and y[n]. (b) For x[n] = [n], find r[n] for all n. (c) Find the system impulse response. P6. 8 Consider the system shown in Figure P6. 8. Find the differential equation relating x(t) and y(t). x(t) + r(t) + y t a Figure P6. 8 b Signals and Systems P6-4 P6. 9 Consider the following difference equation: y[n] ly[n 1] = x[n] (P6. 9-1) (P6. 9-2) with x[n] = K(cos gon)u[n] Assume that the solution y[n] consists of the sum of a particular solution y,[n] to eq. (P6. 9-1) for n 0 and a homogeneous solution yjn] satisfying the equation Yh[flI 12Yhn 1] = 0. (a) If we assume that Yh[n] = Az, what value must be chosen for zo? (b) If we assume that for n 0, y,[n] = B cos(Qon + 0), what are the values of B and 0? [Hint: It is convenient to view x[n] = Re{Kejonu[n]} and y[n] = Re{Yeonu[n]}, where Y is a complex number to be determined. P6. 10 Show that if r(t) satisfies the homogeneous differential equation m d=r(t) dt 0 and if s(t) is the response of an arbitrary LTI system H to the input r(t), then s(t) satisfies the same homogeneous differential equation. P6. 11 (a) Consider the homogeneous differential equation N dky) k~=0 dtk (P6. 11-1) k=ak Show that if so is a solution of the equation p(s) = E akss k=O N = 0, (P6. 11-2) then Aeso is a solution of eq. (P6. 11-1), where A is an arbitrary complex constant. (b) The polynomial p(s) in eq. (P6. 11-2) can be factored in terms of its roots S1, ,S,. : p(s) = aN(S SI)1P(S tiplicities. Note that S2)2 . . . (S Sr)ar, where the si are the distinct solutions of eq. (P6. 11-2) and the a are their mul ­ U+ 1 o2 + + Ur = N In general, if a, ;gt; 1, then not only is Ae a solution of eq. (P6. 11-1) but so is Atiesi as long as j is an integer greater than or equal to zero and less than or Systems Represented by Differential and Difference Equations / Problems P6-5 equal to oa 1. To illustrate this, show that if ao = 2, then Atesi is a solution of eq. (P6. 11-1). [Hint: Show that if s is an arbitrary complex number, then N ak dtk = Ap(s)te t + A estI Thus, the most general solution of eq. P6. 11-1) is p ci-1 ( i=1 j=0 Aesi , where the Ai, are arbitrary complex constants. (c) Solve the following homogeneous differential equation with the specified aux ­ iliary conditions. d 2 y(t) 2 dt2 + 2 dy(t) + y(t) = 0, dt y(0) = 1, y'() = 1 MIT OpenCourseWare http://ocw. mit. edu Resource: Signals and Systems Professor Alan V. Oppenheim The following may not correspond to a parti cular course on MIT OpenCourseWare, but has been provided by the author as an individual learning resource. For information about citing these materials or our Terms of Use, visit: http://ocw. mit. edu/terms.

Prostitution and Functionalism Essay -- Functionalist Theory Prostitut

Prostitution and Functionalism Works Cited Not Included Throughout America and the entire world, prostitution flourishes. Prostitution is another never ending war like abortion, which society feels is immoral. This immorality leads functionalists, who apply functionalism to this social problem, on a chase to figure out why prostitution is what it is today. Functionalism is the best theory for looking at prostitution. It allows us to see how prostitution changes along with other aspects of society.   Ã‚  Ã‚  Ã‚  Ã‚  Some ask why prostitution spreads like a wildfire through our cities and streets. This is an easy question for functionalists, prostitution flourishes because it satisfies sexual needs that are not able to be met elsewhere(Henslin 51). Prostitutes almost seem to serve as an outlet for sexually frustrated men. When a man is unable to find a partner he always holds the option of paying for sexual pleasure. A functionalist, Kingsley Davis, concluded that prostitutes provide a sexual outlet for men who: have difficulty in establishing sexual relationships, cannot find long-term partners, have a broken relationship, want sexual gratification that is defined as immoral, desire quick sexual gratification without attachment, are curious, and are sexually dissatisfied in marriage. From this it is shown that by meeting such needs prostitution functions as a form of social control over sexual behavior. This is beneficial because it brings men with sexual desires away from un wi...

Tiger Mom Essay

In reading â€Å"Battle Hymn of the Tiger Mom† by Amy Chua, I was surprised how Chua shared in detail about her life journey as a parent and raising two children. This is a book about Amy Chua’s experiences in raising her two daughters, Sophia and Luisa (Lulu), in what she believes is the â€Å"Chinese mother† style of parenting. She is quick to point out in the first chapter, entitled â€Å"The Chinese Mother,† that she uses the term â€Å"loosely† as it would be ridiculous to try to assume that every mother from China is a like a tiger mom.Just as â€Å"Western parents† would not be an appropriate label to place on every parent from Western countries. In this same chapter she references a study where â€Å"50 Western American mothers and 48 Chinese immigrant mothers† were polled on the role of parents in children’s academic success; with â€Å"70% of Western mothers believed ‘stressing academic success is not good for t he children’ or ‘parents need to foster the idea that learning is fun’† versus nearly â€Å"0% of the Chinese mothers felt the same way.† Although she states there are several studies that support this theory, I would not put too much credence in this particular study since the pool is too small and there are a lot of â€Å"Western American mothers† with different style of parenting. A â€Å"Western American mother† can be from as far west as Hawaii or from as northeast as Maine; then there is everyone in between.She also gives us a list of what a Chinese mother’s belief system entails: â€Å"schoolwork always comes first; an A-minus is a bad grade; your children must be two years ahead of their classmates in math; you must never compliment your children in public; if your child ever disagrees with a teacher or coach, you must always take the side of the teacher or coach; (6) the only activities your children should be permitted to do are those in which they can eventually medal; and that medal must be gold. † This list seems a little extreme to me, but I guess it just depends on what you are brought up to believe is the norm.When you do not know anything different, this is normal, expected and accepted. As I began to read the book, I quickly realized Amy Chua is very pro â€Å"Chinese† parenting style. In chapter four, â€Å"The Chuas,† she described how her and her sisters were to speak only in Chinese in the home; â€Å"drilled math and piano everyday;† and they were not allowed to attend sleepovers at friends’ homes. Yet, she also tells of the time when she forged her father signature in order to apply to a school in the East Coast after her father had already said she was going to attend the University of California at Berkeley, where he was a professor.Here I saw a bit of a rebellion, which she will come to see later in the book with her daughter Lulu. Throughout the book, I saw many examples of how Chua compared â€Å"Chinese† parenting to â€Å"Western† parenting. This is especially true in chapter 10, â€Å"Teeth Marks and Bubbles. † She tells the story of how she had called her eldest daughter, Sophia, garbage for something Chua believed to be â€Å"extremely disrespectful†, although she never mentioned the offense. She says her father had called her the same thing when she was disrespectful to her mother. However, according to her, it did not damage her self-esteem.However, when she retold this story at friend’s dinner party, she was immediately looked upon with disdain and felt shunned by those around her. She goes on stating the three big differences between the mindsets of Chinese and Western parents. First, Western parents worry about a child’s self-esteem and are more concerned with the child’s psyche, whereas Chinese parents don’t. Chinese parents â€Å"assume strength, not fra gility, and as a result they behave very differently. † Second, Chinese parents feel their children should be indebted to them for the sacrifices the parents made on their children’s behalf.Therefore, they â€Å"must spend their lives repaying their parents by obeying them and making them proud. † Most Western parents do not feel the need to apply that same pressure on their children. Third, Chua claims Chinese parents believe they know what is best for their children and feel entitled to supersede all of their children’s choices and/or decisions. In this particular instance, I believe a most parents, not only Chinese parents, believe they know what is best for their children. Chinese parents take it a step further and do not allow choices for their children, whereas Western parents do allow their child to have choices.Although Chua argues in favor of the Chinese parenting style, she is merely stating the differences between the two approaches and the one she prefers. She lets us into her world and walks us through her trials and tribulations with the â€Å"Chinese mother† approach she elected to follow. Where this style of parenting had worked with her and her sisters and to some extent her eldest daughter, Sophia, however Lulu was not so accepting. Near the end of the book, specifically in Chapter 31 â€Å"Red Square,† everything comes to a boil as she has, yet, another fight with Lulu at the GUM cafe.After the fight, Chua runs away into the Red Square to be with her thoughts, then has an epiphany and realizes that Lulu was rebelling against her and her â€Å"Chinese mother† style of parenting. When she returns to the cafe, she informs Lulu that she had won and she would be allowed to make her own choices and quit the violin. Do I favor this type of parenting? The style of parenting Chua describes in her memoir is that of an authoritarian parenting style, which â€Å"emphasizes high standards and a tendency to control kids through shaming, the withdrawal of love, or punishments† (http://www.parentingscience. com/chinese-parenting. html).This style I do not agree with. In fact, according to Dr. Gwen Dewar, â€Å"authoritarian parenting is linked with lower levels of self-control, more emotional problems, and lower academic performance. † Dr. Dewar is more in favor of an authoritative parenting that involves the same emphasizes of high standards, but also involves â€Å"parental warmth and a commitment to reason with children† (http://www. parentingscience. com/chinese-parenting. html).There is nothing wrong with wanting the best for your children, wanting them to succeed and instilling a hard-work ethic and providing guidance, however it should not be at the expense of the child’s psychological well being. Even though it looks like Chua’s daughter, Sophia, had benefited from this style of parenting, they may just begin to realize they could have possibly achieved the same results without the extreme harassment. Only time will tell if Chua’s daughters will end up resenting her as her father ended up resenting and detaching himself from his family after disagreeing with his authoritarian mother.Especially Lulu, who was the most difficult one. As stated in the beginning, this is a book on how a â€Å"Chinese mother† style of parenting was used by Amy Chua and the results she had with this style. Although, I may not agree with all of the aspects of this style, it does have its pros; such as wanting your child to the best that they can be and its cons; such as the belittling of a child can never be good. This was never intended to be a â€Å"How to Guide† to parent your children, as Chua stated in an interview after the book was released (http://abcnews. go.com/US/tiger-mother-amy-chua-death-threats-parenting-essay/story? id=12628830).Chua has received a lot criticism from many people, but I agree with her, this is n ot a guide to parent a child. The reason being is that each child is unique in its own way. What may be a good approach for one, it not necessarily good for another. As she acknowledged in her book, â€Å"When Chinese parenting succeeds, there’s nothing like it. But it doesn’t always succeed. † However, at the end of the day you make the decision you feel is right for you and your family and adjust, as needed, as you go along.

Easy To Make Glitter Slime

Why make ordinary slime, when you can make sparkly glitter slime!  Try this easy recipe to make the slime in any color of the rainbow. Materials Glitter glueBoraxWater The recipe works with either clear or white school glue, but white glue makes opaque slime. For clear or translucent colored slime that glitters, choose a clear or translucent glue. If you cant find glitter glue, add glitter as an ingredient. Borax is sold as a detergent booster with laundry supplies, or you can purchase it online. Making Glitter Slime Slime is a polymer that forms when you mix two solutions: glue and dissolved borax. The first step is to make these solutions. Dissolve 1 teaspoon borax in 1/2 cup warm water. Its okay if the borax doesnt completely dissolve. You only need the liquid part, not any solid that stays at the bottom of the cup.In a separate container, mix 1/2 cup glue (4-oz bottle of glue) and 1 cup of water. If you dont like the color of the slime, you can add a few drops of food coloring to the mixture.When you are ready to make glitter slime, dump the two mixtures into a bowl. Use your hands to mix the slime (thats part of the fun). If you have any leftover liquid after the slime polymerizes, you can discard it. When you are finished playing with the glitter slime, you can store it in a sealed plastic bag. The borax is a natural disinfectant, but the slime will keep fresh even longer if you refrigerate it. Clean-up is easy using warm water.