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20092ee102_1_S09-102-HW-4

20092ee102_1_S09-102-HW-4 - Spring 2009 Put First Letter of...

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Spring 2009: Put First Letter of LAST Name in the corner →→%% ( Otherwise Your HW Will Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– EE102: SYSTEMS & SIGNALS HW: # 4 A LATE HW IS A NON-HW! Posted: April 23 Hand In To Me 1 : April 30 Attach This Sheet To Your HW (Otherwise It Will Be Lost!) 1. Solve the DE, together with the given initial conditions, by LT: d 2 y ( t ) dt 2 + 3 dy ( t ) dt + 3 y ( t ) = U ( t ) , t > 0 and y (0) = 0 , ˙ y (0) = 1 (iii) Find f ( t ) given that: F ( s ) = s + 1 s 3 + 6 s 2 + 4 s F ( s ) = s 2 + 4 s s 2 + 2 s + 2 2. Find the Laplace Transform F ( s ) of f ( t ) given that f ( t ) = cos t Z t 0 cos τ d τ + sin t Z t 0 cos τ d τ , t > 0 3. Find h ( t ) given that its Laplace Transform H ( s ) is H ( s ) = s 2 s 2 + s + 4 1 during the break of the Thursday Lecture 1

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If H ( s ) is the System Function of a LTIC system, write down the di ff erential equation relating its input x ( t ) and its output y ( t ). 4. The PZP (Poles-Zeroes-Plot) of the LT H ( s ), of the IRF h ( t ), of a LTIC system S , has the following characteristics: zero of order 1 at : 3 pole of order 1 at : 1 pole of order 2 at : 2 H (0) = 3 2 (i) Find h ( t ) then write down the IPOP relation of S . (ii) Find the IP x ( t ) given that the OP is y ( t ) = [ 5 e 2 t + 5 4 e t 4 e t t ] U ( t ) (iii) Consider:
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