Gate 2016 EE (Set 1) Q3

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

Solution:

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

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