20092ee102_1_S09-102-HW-3

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

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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 ) 2 U ( t ) U ( ) d, 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...

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