Question

If f(t) = cos(at) + atsin(at), its Laplace transform is given by?

(a) \(\frac{s+a}{s-a}\)

(b) \(\frac{a^3}{(s^2+a^2)^2}\)

(c) \(\frac{s(s^2+3a^2)}{(s^2+a^2)^2}\)

(d) Does not exist

I have been asked this question in an interview for job.

This interesting question is from Existence and Laplace Transform of Elementary Functions in section Laplace Transform of Engineering Mathematics

Answer 1

Correct choice is (c) \(\frac{s(s^2+3a^2)}{(s^2+a^2)^2}\)

To elaborate: 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) = cos(at) + atsin(at) to solve the problem.