# HW15

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Signals and Systems 28 November 2012 Fall 2012 Quiz: Wednesday 5 December 2012 Homework Assignment #15 1. Find the inverse Laplace transform of each of the following functions. (a) 25 6 2 3 ) ( 2 + + + = s s s s X (b) 2 1 ) ( 4 + = s e s X s 2. A system governed by the differential equation ) 4 ( 2 ) ( ) ( ) ( 2 . 0 ) ( + = + + t x t x t y t y t y is initially at rest. The input of the system is Ϊ Ω Ϊ Ψ Χ < < = 2 2 0 0 0 ) ( 2 t e t e t t x t . Find the Laplace transform of the input x ( t ) and of the output y ( t ); i . e ., find X ( s ) and Y ( s ). 3. A system has the transfer function ) 100 12 ( 100 ) ( 2 + + = s s s s H . (a) Sketch the pole-zero plot of H ( s ). (b)
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