20092ee102_1_S09-102-HW-3

# 20092ee102_1_S09-102-HW-3 - Spring 2009 Put First Letter of...

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Unformatted text preview: 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: # 3 A LATE HW IS A NON-HW! Posted: April 16 Hand In To Me 1 : April 23 Attach This Sheet To Your HW (Otherwise It Will Be Lost!) 1. (i) Calculate the Laplace Transforms (LT) of t 2 e − t U ( t ) , e − 2 t cos tU ( t ) , (ii) What can you say after you have compared your results in (i) with the LT of t 2 U ( t ) and that of cos tU ( t ), respectively? Hint: Use the definition of LT. Do not forget the DOC (Domain Of Conver- gence). 2. (i) Calculate the convolution integral: y ( t ) = Z ∞ −∞ ( t − σ ) 2 U ( t − σ ) σ U ( σ ) dσ, t ∈ ( −∞ , ∞ ) . Then compute the Laplace Transform of y ( t ) — which you just (hopefully “correctly”) calculated. (i) Next, compute the product: L s { t 2 U ( t ) } . L s { tU ( t ) } Do you find: L s { y ( t ) } =...
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20092ee102_1_S09-102-HW-3 - Spring 2009 Put First Letter of...

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