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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, timeshifted 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
zerostate 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 zerostate 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 zerostate
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 mII. 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. Balm1.1; (25 points) For a certain second order, LTI system, the following observations were made: 2 —— wastum
— us+4=w+41um Question 4.1 (9 points) Find the zerostate response when ﬁt) = u(t). Place your answer in the box provided. mt) = Question 4.2 (9 points) Find the zeroinput 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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 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB

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