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Gate 2016 EE (Set 1) Q3

Gate 2016 EE (Set 1) Q3

3. The Laplace Transform of  f(t)=e^2t Sin(5t)u(t)  is :--------

Solution:

 f(x)=e^2t sin?(5t)u(t)
 L{e^at sin??t }= ?/((s-2)^2+?^2 )
 a=2
 ?=5
 L{e^2t sin?(5t) }=5/((s-2)^2+5^2 )=5/(s^2+4-4s+25)=5/(s^2-4s+29)

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