Question

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

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

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

(c) Indeterminate

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

I have been asked this question in an online quiz.

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

Answer 1

The correct choice is (d) \(\frac{2as^2}{(s^2+a^2)^2}\)

Easiest 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) – atcos(at)

On solving, we obtain 2as^2 ⁄ (s^2+a^2)^2