Question

If f(t) = tcos(at), its Laplace transform is given by?

(a) 1 ⁄ s-a

(b) s^2 – a^2 ⁄ (s^2+a^2)^2

(c) Indeterminate

(d) s^2at

This question was addressed to me during an online interview.

My question is taken from Existence and Laplace Transform of Elementary Functions topic in chapter Laplace Transform of Engineering Mathematics

Answer 1

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

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) = tcos(at)

On solving the above integral, using suitable rules of integration we get the answer s^2 – a^2 ⁄ (s^2+a^2)^2.