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20085ee102_1_F08-102-HW-4

# 20085ee102_1_F08-102-HW-4 - FALL 2008 Put First Letter of...

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FALL 2008: Put First Letter of LAST Name in the corner →→ ( Otherwise Your HW May Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– EE102: SYSTEMS & SIGNALS HW: # 4 A LATE HW CANNOT BE A HW! Posted: W, October 22 Hand In To Me: M, November 3 Attach This Sheet To Your HW (Otherwise It May Be Lost!) Instructions: (i) Please hand in Problems: 1, 3, 5, 7, and 8. (ii) Problems: 2, 4, 6, and 9 (taken from Past MT) are Review Problems. 1. (i) We have computed L s { df ( t ) dt } and L s { d 2 f ( t ) dt 2 } . Now it is your turn to compute L s { d 3 f ( t ) dt 3 } . Use your result to conpute the LT of d 3 f ( t ) dt 3 , where f ( t ) = t sin 2 t U ( t ) (ii) Compute Y ( s ), the Laplace Transform of y ( t ), given d 2 y ( t ) dt 2 + 3 dy ( t ) dt + y ( t ) = cos 2 t, t > 0 , and y (0) = 1 , ˙ y (0) = 0 . (iii) Find f ( t ) given that: F ( s ) = s + 2 s 2 + 7 s + 12 , F ( s ) = s + 1 s 3 + 5 s 2 + 7 s , F ( s ) = 2 s 2 - 9 s - 35 s 2 + 4 s + 2 . 1

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2-RP. Let h ( t, τ ) be the IRF of a Linear system. If the system is TI and C then h ( t, τ ) is of the form: h ( t, τ ) = h ( τ - t ) U ( τ - t ) True or False? Why?
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