examI_s99

examI_s99 - EXAM 1 EE 350 15 February 1999 Name (Print): ID...

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Unformatted text preview: EXAM 1 EE 350 15 February 1999 Name (Print): ID # : Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO TEST FORM A Instructions: 1. You have 2 hours (120 minutes total) to complete this exam. 2. This is a closed book exam. However, as told earlier, you are allowed 1 sheet of 81/22” x 11” paper for notes, formulas, etc... 3. Solve each part only in the space following each question. Be sure to place your answers in the boxes (as appropriate) provided. If you need more space, continue on the reverse side and write the question number; for example, Question 4.21 continued”; N0 credit will be given to a solution that does not meet this requirement. 4. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will NOT be accepted and a grade of ZERO will be assigned. Pmmgg 1: (25 points) Question 1.1 (5 points) Write a analytical expression for the signal, f1(t), given in Figure L Place your answer in the box provided. f1(t) Figure l — Signal, Mt). Question 1.2 (5 points) Express the signal, f2(t), given in Figure 2, in terms of linear, time-shifted combinations of 116) from Question 1.1 above. Place your answer in the box provided. 66) Figure 2 ~— Signal, fz(t). Question 1.3 (5 points) Suppose the signal, f1(t), from Question 1.1 was applied to an LTI system and the resulting zero-state response, y;(t), was found to be y1(r)= 4e‘2'ua). Now, the signal, f2“), fi'om Question 1.2 is applied to the same LTI system. Obtain the analytical expression for the zero-state response, y2(t)l Place your answer in the box provided. Question 1.4 (5 points) Using the signal. f;(t), fi'om Question 1.1 above, sketch the signal, 13(1) = 2mg“) in the graph provided in Figure 3. Figure 3 — Blank graph for sketching f3(t). Question 1.5 (5 points) A periodic current waveform, i(t), shown in Figure 4, is applied to a 5 Q resistor. Find the average power dissipated by the resistor. Place your answer in the box provided. Figure 4 - Current waveform, i(t). Problem 2: (25 points) Question 2.1 (15 points) An LT! system, shown in Figure 5, is excited by {(t) = 10eos(3 St) and has a zero-state response, y(t) = cos(35t + 703). fit) LT] V“) Figure 5 —~ The system for Question 2.1. A new input, f. (t) = 2005(3 5t + 31:14) - Ssin(35t), is applied to the same system. Determine the zeronstate output, y.(t). Place your answer in the box provided. Question 2.2 (5 points) Give an example of a causal system that has memory. Question 2.3 (5 points) A certain system is described by the ordinary differential equation: 42y a)” dzf df _3...._._ .. _ — 6 I : 3w 6— t at:2 d: y” at2 + d: + f() Is this system asymptotically stable? Justify your results. Prghlgm 3: (25 points) Questions 3.1 and 3.2 use the circuit shown in Figure 6. The value for the resistor is R=600 fl and the value for the inductor is LE3 mI-I. f6) 0 ye) Figure 6 —— Circuit for Questions 3.1 and 3.2 Question 3.1 (7 points) Find the ordinary differential equation that relates the input current, fit), to the output current, y(t). Your final answer must be in standard form. Place your answer in the box provided. Solution for (23.1: Question 3.2 (7 points) Let f(t) = 0.0](3u(-t) + 7631116)). Find vc(0+), y(0+), and g—l . Be sure to give l=0+ appropriate units for each answer. Place your answers in the boxes provided. . Questions 3.3 and 3.4 use the system whose model is given by (le + 21D + 216) y(t) = (so + 2) in) Question 3.3 (3 points) Determine (on, I; and, if the system is underdarnped, 03d. Be sure to give appropriate m for each answer. Place your answers in the box provided. Question 3.4 (3 points) Let in) = 365‘ u(t). a) Find the particular solution, yp(t), fort > 0. Piece your answer in the box provided. b) Find the m of the homogeneous solution, yh(t), fort > 0. (Initial conditions are not specified so your solution may contain unknown coefficients.) Place your answer in the box provided. Balm-1.1; (25 points) For a certain second order, LTI system, the following observations were made: 2 —--— was-tum —- us+4=w+41um Question 4.1 (9 points) Find the zero-state response when fit) = u(t). Place your answer in the box provided. mt) = Question 4.2 (9 points) Find the zero-input response of the system when the initial states are xl(0) = 8 and xz(0) = 8. Place your answer in the box provided. hi0) = Question 4.3 (2 points) Determine the natural fi'equencies of the system, it, and 14;. Place your answers in the boxes provided. Question 4.4 (5 points) From the above observations, determine whether it is possible or impossible to write the ordinary differential equation system model. It is known that the system model does not contain derivatives of the input, fit). If it is possible, then write the exact ODE in proper form. Ifit is impossible, then clearly explain why. (Hint: Focus on how the forced response is determined from ODE system models.) ...
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examI_s99 - EXAM 1 EE 350 15 February 1999 Name (Print): ID...

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