Question

Find the laplace transform of e^t Sin(t).

(a) \(\frac{a}{a^2+(s+1)^2}\)

(b) \(\frac{a}{a^2+(s-1)^2}\)

(c) \(\frac{s+1}{a^2+(s+1)^2}\)

(d) \(\frac{s+1}{a^2+(s+1)^2}\)

I got this question during an online interview.

I'd like to ask this question from Laplace Transform by Properties in chapter Laplace Transform of Engineering Mathematics

Answer 1

Correct option is (b) \(\frac{a}{a^2+(s-1)^2}\)

Best explanation: F(s)=\(\int_{-\infty}^\infty e^t sin⁡(at)u(t) e^{-st} dt=∫_0^∞ sin⁡(at)e^{-(s-1)t} dt\)

=\(\left [\frac e^{-st}{a^2+(s-1)^2} [-(s-1)sin(at)-acos⁡(at) ]\right ]_0^∞\)

=\(\frac{a}{a^2+(s-1)^2}\)