ECE2260F10_HW6p1soln

Next we apply the following identity for

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Unformatted text preview: on the delayed delta function. Next, we apply the following identity for multiplication by t: L{tf ( t )} = − d F ( s) ds Here, we have the following result: L{t cos(9 t )} = − d s −1 s(2 s) =2 +2 2 2 2 ds s + 9 s +9 [ s + 9 2 ]2 We sum the results for the final answer: 1 2s2 L{δ( t − 4 ) u( t − 4 ) + t cos(9 t )} = e−4 s − 2 +2 s + 9 2 [ s + 9 2 ]2 b) We first factor the denominator. s2 + 10 s + 25 = ( s + 5) 2 We can take the inverse transform immediately for this form of denominator: ⎧ 16 ⎫ v ( t ) = L -1 ⎨ ⎬ = 16 te−5t u( t ) 2 ⎩ ( s + 5) ⎭ [ NOTE: We multiply by u(t) to sugge...
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This document was uploaded on 03/17/2014 for the course ECE 2260 at Utah.

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