What is the analytic expression of $f(t)$ which is defined as the following inverse Laplace transformation:
$$ f(t)=L^{-1}{\Bigg\{ {w\over {w^2+s^2}}\cdot {e^{bs}-e^{-bs}\over{e^{as}-e^{-as}}} \Bigg\}} $$
where $w$, $a$ and $b$ are constants. Note that $a$ is greater then $b$.
It seems to me that it is probably a convolution of a sine function and one more function. But I am not able to determine which one.