Question

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

(a) Indeterminate

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

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

(d) \(\frac{2a^3}{(s^2+a^2)}\)

This question was posed to me in an interview for internship.

I'd like to ask this question from Existence and Laplace Transform of Elementary Functions topic in division Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (b) \(\frac{(s)sin(b)+acos(b)}{s^2+a^2}\)

The explanation is: 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) = sin(at + b) to solve the problem.