hw02-3723-06f - ECEN/MAE 3723 Systems I Fall 2006 Homework...

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ECEN/MAE 3723 Systems I Fall 2006 Homework Assignment #2 Problem 1 : Derive the Laplace transform of the following signals. (Do not use integral definition, use transform table and properties) a) ) ( 5 5 t u te t , b) ( ) ) ( 2 sin 2 t u e t t t + , c) ) 1 ( )) 1 ( 2 sin( t u t , d) ) 1 ( ) 1 ( ) 1 ( t u e t t a e) ) ( 2 ) ( c t u e b t a , f) ) ( ) ( sin 5 c t u b t a Problem 2 : Derive Laplace transform theorem on t - multiplication and t - division : a) () ds s dX t tx ) ( ) ( = L , and b) L xt t Xd s ⎟ = ξξ
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