Question

If f(t) = ^t⁄2 a sinat, then its Laplace transform is?

(a) b ⁄ (s + a)^2 + b^2

(b) 2a ⁄ (s – b)^2 + b^2

(c) Indeterminate

(d) s ⁄ (s^2 + a^2)^2

I had been asked this question in my homework.

My doubt stems from Existence and Laplace Transform of Elementary Functions in chapter Laplace Transform of Engineering Mathematics

Answer 1

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

To 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) = t⁄2a sinat

Integrate to obtain, the required transform s ⁄ (s^2 + a^2)^2.