Question

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

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

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

(c) \(\frac{scos(b)-asin(b)}{s^2+a^2}\)

(d) Does not exist

This question was addressed to me during an interview.

Origin of the question is Existence and Laplace Transform of Elementary Functions in section Laplace Transform of Engineering Mathematics

Answer 1

Correct option is (c) \(\frac{scos(b)-asin(b)}{s^2+a^2}\)

For explanation I would say: 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 + b) to solve the problem.