Question

If f(t) = e^at sin(bt), then its Laplace transform is given by?

(a) s^2-a^2 ⁄ (s – a)^2

(b) b ⁄ (s + a)^2 + b^2

(c) b ⁄ (s – a)^2 + b^2

(d) Indeterminate

This question was addressed to me in an interview for job.

This key question is from Existence and Laplace Transform of Elementary Functions topic in chapter Laplace Transform of Engineering Mathematics

Answer 1

Right option is (c) b ⁄ (s – a)^2 + b^2

Easiest explanation: The Laplace transform of a function is given by

\(\{f(t)\}=F(s)=\int_0^{\infty} f(t)e^{-st}dt\)

put f(t) = e^atsin(bt)

On solving, we get the b ⁄ (s – a)^2 + b^2.