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Find the response of a system with transfer function

H(s)=1s+5Re(s)>5 Input x(t)=etu(t)+e2tu(t)

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : MAY 2014

1 Answer
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By Laplace transform,

X(s)=1(s+1)+1(s+2)=2s+3(s+1)(s+2)Y(s)=x(s)×H(s)=2s+3(s+5)(s+1)(s+2)

By partial fraction,

Y(s)=As+1+Bs+2+Cs+5

On solving we get,

A+B+C=0(1)7A+6B+3C=2..(2)10A+5B+2C=3(3)

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Y(s)=0.583s+5+0.25s+1+0.33s+2

By Inverse Laplace transform,

y(t)=0.583e5tu(t)+0.25etu(t)+0.33u(t)  for  ROC  Re(S)>5.

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