Question

If f(t) = e^at cos(bt), then its Laplace transform is?

(a) 2a^3 ⁄ (s^2 + a^2)

(b) s+a ⁄ s-a

(c) Indeterminate

(d) s-a ⁄ (s – a)^2 + b^2

I got this question during an online interview.

My query is from Existence and Laplace Transform of Elementary Functions in portion Laplace Transform of Engineering Mathematics

Answer 1

The correct option is (d) s-a ⁄ (s – a)^2 + b^2

For explanation: The Laplace transform of a function is given by

\(\{f(t)\}=F(s)=\int_0^{\infty} f(t)e^{-st}dt\)

put f(t) = e^atcos(bt)

Solve the above integral, to obtain s-a ⁄ (s – a)^2 + b^2.