Question

If f(t)=\(\frac{1}{b}e^{at}sinh(bt)\), then its Laplace transform is?

(a) 1/s

(b) Indeterminate

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

(d) \(f(t)=\frac{1}{(s-a)^2-b^2}\)

I had been asked this question in unit test.

This is a very interesting question from Existence and Laplace Transform of Elementary Functions in section Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (d) \(f(t)=\frac{1}{(s-a)^2-b^2}\)

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

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

put f(t) = 1⁄b e^atsinh(bt) to solve the problem.