Question

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

(a) s ⁄ s^2+a^2

(b) a ⁄ s^2+a^2

(c) √π ⁄ 2√s

(d) Does not exist

I got this question in an international level competition.

My question is based upon Existence and Laplace Transform of Elementary Functions topic in section Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (a) s ⁄ s^2+a^2

For 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) = cos(at)

On solving the above integral, we get s ⁄ s^2+a^2.