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For the given LTI system, described by the differential equation:

dy2(t)dt2+3dy(t)dt+2y(t)=x(t) Calculate output y(t) if input x(t)=e3tu(t) is applied to the system.

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : MAY 2014

1 Answer
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By Laplace transform,

X(s)=1s+3

By Laplace transform,

$s^2y (s) +3s\space y (s) + 2 y (s) = x (s) \\ y (s)(s^2+3s+2) = x (s) \\ H (s) = \dfrac 1{(s^2+3s+2)} \\ =\dfrac 1{(s+1)(s+2) } \\ Y (s) = x (s) \times H (s) \\ =\dfrac …

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