20065ee102_1_102-F06-HW3[1]

20065ee102_1_102-F06-HW3[1] - FALL 2006 Put First Letter of...

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Put First Letter of LAST Name in the corner →→→% Name (LAST, Middle, First):———————— ——————————— HW :#3 ALATEHWISNOTAHW ! Posted: October 18 Hand In: October 25 Attach This Sheet To Your HW 0. Calculate the Laplace Transforms of those functions on the Table (in the Text) which have NOT been calculated for you in class! In each case clearly indicate the DOC on the PZP of the transform. 1. Find the Laplace Transform of the following signals: (i) e 2 t sinh5 tU ( t ) (ii) e t cos( t π 3 ) U ( t ) (iii) ( e αt sin 2 ω 0 t ) U ( t ) > 0 . 2. Show the following properties of L s ( · ): (i) Scaling: F ( s )= L s { f ( t ) }⇒L s { f ( at ) } = 1 a F ( s a ) , for a> 0 . (ii) Multiplication by t : L s { tf ( t ) } = d ds F ( s ) . 3. Calculate the following integral: y ( t )= Z −∞ e ( t σ ) U ( t σ ) σU ( σ ) dσ, t 0
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20065ee102_1_102-F06-HW3[1] - FALL 2006 Put First Letter of...

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