Question

Find Laplace transform F(p) for function (show all work)
f(t)=exp(-at)sh(wt)

Answer 1

By translation theorem:

$$\begin{array}{l} sh(w t) \rightarrow \frac{w}{p^{2} - w^{2}} \\ e^{-at} sh(w t) \rightarrow \frac{w}{(p + a)^{2} - w^{2}} \\ \end{array}$$