Differential Equation free essay sample

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 partic ular 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.

Richard Nixon Paper free essay sample

Richard Onions early life was hard. He always described his family as being poor. The family experienced tragedy early in Richards life when his younger brother died in 1925 after a short illness and later when he was 20, his older brother, died of tuberculosis ;n 1933. Richard Nixon attended Fullerton High School but later transferred to Whittler High School. There he ran for student body president, but lost. Nixon graduated high school second In his class and was offered a scholarship to Harvard. But his family couldnt afford the travel and living expenses so he attended local Whittler College, aQuaker Institution. This Is where he earned a reputation as a formidable debater and standout in college drama productions as well as successful athlete. Upon graduation from Whittier in 1934, Nixon received a full scholarship to Duke university Law School. After Duke he returned to Whittier to practice law at the firm of Crook Belly. We will write a custom essay sample on Richard Nixon Paper or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page He met Thelma Catherine Ryan, a teacher and amateur actress, after the two were cast in the same play at a local community theatre. The couple married in 1940 and had two daughters, Iatric and Julie.Being a lawyer in a small town was not enough for Nixon, so he decided to move myself and his family to Washington DC, where he took a job in Franklin Roosevelt Office of Price Administration. Nixon then Joined the navy, serving as an aviation ground officer In the Pacific. After his return to the united States Nixon was approached by a group of Republicans who encouraged him to run for Congress. Nixon was elected to the U. S. House of Representatives in November, 1946. In 1950, Nixon successfully ran for the united States Senate against Democratic Rep. Helen Ghana Douglas.Richard Onions anti-communist reputation earned him the notice of Dwight D. Eisenhower and the Republican Party, believing he could win support in the West. At the Republican convention in 1952, Nixon won the nomination as vice president. In 1968, Richard Nixon became the Republican candidate for President with Spiro Agene as his Vice President. He defeated Democrat Hubert Humphrey and American Independent George Wallace. Nixon received 43% of the popular vote and 301 electoral votes. In 1972, he was the obvious choice for ornamentation with Agene as his running mate again. He was opposed by Democrat George McGovern.

Understanding Your Strengths and Weaknesses

Understanding Your Strengths and WeaknessesRemembering your strengths and weaknesses is just as important as taking a test. When preparing for your AP tests, you will find that one of the most difficult parts of your essay is coming up with reasons to change your answer from one statement to another. You need to stay true to your position even if it is obvious that you are already doing so.Once you have been exposed to all of your strengths, then the first step is to discover your weaknesses. Your strengths might include writing skills or an ability to learn quickly. If you think about your weaknesses and how they affect your life, this is the place to begin thinking about the best solution to these problems.Remembering your strengths and weaknesses can be done while you are in class. Go over what you know about them and make sure that you are happy with the areas you possess. Use examples that will really demonstrate your knowledge about them. It is important to stay in control at a ll times when it comes to the essay.Some people might like to just take a few practice test questions and use that information in the essay. This might work but you are going to find that the process of testing yourself on paper will be harder than it has to be. Instead of going back and forth with yourself, you should make sure that you just prepare your thoughts and words before you start writing the essay.In order to be successful with both your strengths and weaknesses, you need to understand how to make sense of them. If you simply look at something for a long time without being able to put together the details, you will tend to write an incoherent thought. You need to first put your focus on getting the basics down first before getting too far into the specifics.The second part of writing an essay is to make strong examples out of your strengths. Consider the time that you spent working on improving your writing skills. Find the strong example and use it to build your argument for your own strengths.Writing a sample essay can help you focus your focus on your strengths and weaknesses. It can also help you come up with examples of areas where you might be lacking. Once you have found this area, you can start to write about the strengths you have and the weaknesses you think you have.

Stalin and Idustrialization essays

Stalin and Idustrialization essays Stalin and Industrialization in the 1930s For many countries in Europe during the early nineteen hundreds, industrialization had already left its mark and was considered widespread. Other countries were several steps behind such industrial powers as Great Britain. Their economies still depended on rural markets and there had been no influx of people to urban areas. One country, Russia, had such an economy. Joseph Stalin would soon change this, however. So, in hindsight, the Industrial Revolution was necessary and eminent for the Soviet Union but Stalin forced it on his state in a horrific manner, which only worsened living conditions and created negative tensions among his people. In order to better comprehend the negative aspects of Stalins industrialization, first it is necessary to put the circumstances into perspective with a brief summary of Stalins rise to power, then an overview of the two Five Year Plans will be provided, and finally the effects of Stalins industrialization will be outlined. Stalin first came out of the woodwork during the October Revolution in the early 1900s, with the rise of Lenin and the Bolsheviks. Stalin became general secretary of the Bolshevik party's Central Committee. He was also the commissar of the Workers' and Peasants' Inspectorate and the commissar of nationalities (McCauley 3). The two apparent heirs to Lenin's regime were Josef Stalin and Leon Trotsky. After Lenin's death, Stalin gained power by allying himself with the moderates to fight off his rival, Leon Trotsky, who was a radical and another member of the Central Committee. Although Trotsky was better suited for the position (with his strong political inclinations towards reasonable social adaptability), Josef Stalin assumed control and subsequently ordered the exile of all opposing cabinet ministers, including Trotsky. Anyone in the Union who objected to his decisions was sent to Siberian prison camps ...

International Business Strategy Essay Example | Topics and Well Written Essays - 2000 words

International Business Strategy - Essay Example Wal-Mart is known to be slow in internationalization. It has been flopped in Germany already. Its endeavour into India is full of strategic risks. 2. Wal-Mart has entered into India with a 50-50 partnership with Bhartia, a legendry retail brand. This has minimized Wal-Mart’s own business freedom. 3. Government policies in India have not allowed Wal-Mart to use its brand name and logos. It is a mere back-end supporter, not a retailing brand there. Thus, Wal-Mart is facing a great and risky business challenge in India. It has to be careful enough not to deviate from cultural regulations and norms as it is already facing reservations from patriotic political parties and local retailers being only foreign. Any more deviation might repeat what happened in Germany. To be successful, Wal-Mart has to merge into the national culture so as not to present the image of an alien to the Indian clientele. Introduction Wal-Mart is a U.S based Multinational Corporation, which operates chains o f warehouse stores and discount departmental stores in the U.S and 15 other countries. The company is listed on the NYSE, and is reported to be the world’s largest public corporation by revenue (Forbes Global 2000 as cited in Hayden et al, 2002). Wal-Mart has 8500 stores in 15 countries and has been mostly successful in its venture into the global market. Once asked if Wal-Mart was trying to take over the world, the reply from one of the senior heads from Wal-Mart, with a smile on his face was, â€Å"I don't think so, and all we want to do is grow†. This has been evident from the aggressive growth and expansion strategy adopted by Wal-Mart both within and outside the U.S. It has been expanding with massive momentum, with the strategy of â€Å"Always Low Prices Always† and has taken over the retail industry in many countries. However, it has stumbled in its smooth expansion in countries like Germany, where Wal-Mart became a text book case of â€Å"how not to ent er a foreign market† (Peng, 2009). The success of Wal-Mart in its home country, and a variety of other markets like Argentina, Brazil, Britain, Canada, China, Japan, Mexico and Puerto Rico do not seem to have translated into the German market and therefore, Wal-Mart’s expansion plans must be carefully evaluated before giving them a green signal. Wal-Mart knows that venture into India will not be an easy feat because of the market dynamics. Analysis of Wal-Mart Business Strategies To understand Wal-Mart’s position in international business, an analysis of its internationalization, entry and corporate strategies is must. This analysis is as follows: Firm Motivations for Internationalization Internationalization has always been a risky move. Wal-Mart’s failure in Germany or its initial struggle in Mexico clearly indicates that expansion abroad should be carefully evaluated to see whether going abroad is warranted. Source: Global strategy by Mike Peng Wal-Mart falls in cell 3 and may be termed as slow as it internationalizes. The company is still in exploring locations in U.S. In 2010, it opened about 600 international stores, while only about 150 in U.S. However, its pace of internalization is slower than some of its competitors, like Carrefour in France, or Metro in Germany. According to John B. Menzer, Wal-Mart India’

The difference in rawls and nozick is fundamentally a difference in Essay

The difference in rawls and nozick is fundamentally a difference in what it means to be an indiviudal. what is that difference and how does that difference impact their theories - Essay Example The practice of practice of political and social power should be within the limits of justice. Nozick perspective of justice is a critique of Rawls propositions. Not all members of the society benefit from the social cooperation. Rawls’ theory of justice should be based on the reality that the successful individuals in the society have an upper hand on the less disadvantaged in the society. The reality helps the theory to address diversity better in a liberal society. The theory would assist individuals to orient better in their social world. Nozick’s theory becomes a tool for determining the moral outcomes of individuals in the society. The theory should have a model that can enable people understand society from a broader perspective of justice. Human life is not defined through corruption, prejudice, and cruelty but through free and equality principles (Paul, Miller and Paul

Accident Prevention Program Essay Example for Free

Accident Prevention Program Essay The committee is made up of management-designated representatives and one employee-elected representative each from the office, factory and outside sales divisions of our company. Employees in each division will elect from among themselves a representative to be on the committee. If there is only one volunteer or nomination, the employees will approve the person by voice vote at a short meeting called for that purpose. If there is more than one volunteer or nomination, a secret paper ballot will be used to elect the representative. Elected representatives will serve for one year before being re-elected or replaced. If there is a vacancy then an election will be held before the next scheduled meeting to fill the balance of the term. In addition to the employee-elected representatives, management will designate no more than three representatives but a minimum of one who will serve until replaced by management. A chairperson will be selected by majority vote of the committee members each year. If there is a vacancy, the same method will be used to select a replacement. In addition to the committee responsibilities explained above, duties of safety committee members include: A monthly self-inspection of the area they represent Communicating with the employees they represent on safety issues and Encouraging safe work practices among co-workers. The regularly scheduled meeting time is 7:30 am for one hour on the first Thursday of each month, at the employee lunchroom. This may be changed by vote of the committee. A committee member will be designated each month to keep minutes on the attached minutes form. A copy will be posted on the employee bulletin board after each meeting. After being posted for one month, the minutes will be filed for one year. The minutes form contains the basic monthly meeting agenda. (Customize by adding any additional safety committee information that you may have and/or deleting any that do not apply to your company. ) Employee Safety Meetings (Optional for employers with 10 or fewer employees or employers with 11 employees or more who are segregated on different shifts or work in widely dispersed locations in crews of 10 or less) All employees are required to attend a monthly safety meeting held on the first Thursday of each month in the lunchroom. This meeting is to help identify safety problems, develop solutions, review incidents reports, provide training and evaluate the effectiveness of our safety program. Minutes will be kept on the attached minutes form. Meeting minutes will be kept on file for one year. (Customize by adding any additional Employee Safety Meeting information that you may have and/or deleting any that do not apply to your company. ) Hazard Recognition Record Keeping and Review Employees are required to report any injury or work related illness to their immediate supervisor regardless of how serious.