Question

If f(t) = ^1⁄a sinh(at), then its Laplace transform is?

(a) 1⁄s^2-a^2

(b) 2a ⁄ (s – b)^2 + b^2

(c) n! ⁄ (s – a)^n-1

(d) Does not exist

The question was asked during an internship interview.

The doubt is from Existence and Laplace Transform of Elementary Functions topic in chapter Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (a) 1⁄s^2-a^2

The best I can explain: The Laplace transform of a function is given by

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

put f(t) = f(t) = 1⁄a sinh(at)

On solving the above integral, we get the 1⁄s^2-a^2.