Question

If f(t) = cos(at) – atsin(at), then its Laplace transform is given by?

(a) sinat^2

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

(c) \(\frac{\Gamma(p+1)}{s^{p+1}}\)

(d) Does not exist

The question was asked in exam.

I want to ask this question from Existence and Laplace Transform of Elementary Functions topic in section Laplace Transform of Engineering Mathematics

Answer 1

The correct option is (b) \(\frac{s(s^2-a^2)}{(s^2+a^2)^2}\)

Easy explanation: 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) = cos(at) – atsin(at)

On solving, we obtain a^3 ⁄ (s^2 + a^2)^2.