If $f(t)$ has a Laplace Transform $F(s) = \frac{5}{s^4 + 4s^2}$, find the Laplace Transform for the following
(a) $\mathcal{L}\left\{\frac{df(t)}{dt}\right\}$, assume $f(0) = 0$.
(b) $\mathcal{L}\{e^{-t}f(t)\}$.
(c) $\mathcal{L}\{tf(t)\}$
(d) $\mathcal{L}\{f(t-2)u(t-2)\}$