Question

If f(t) = sin(at), then its Laplace Transform is given by?

(a) cos(at)

(b) 1 ⁄ a^sin(at)

(c) Indeterminate

(d) a ⁄  s^2+a^2

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

Question is from Existence and Laplace Transform of Elementary Functions in division Laplace Transform of Engineering Mathematics

Answer 1

Right option is (d) a ⁄  s^2+a^2

Easy explanation: The Laplace Transform of a functions is given by

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

Put f(t) = sin(at)

On solving, we get a ⁄  s^2+a^2.