$\left(b\right)$ Find the Laplace Transform of the function of period a defined $by:$ $f\left(t\right)=1$ $,$ when $0<t<\dfrac {a} {2}$ $=-1$ $1$ when $\dfrac {a} {2}<t<a$

Find the Laplace transform of the function $sinh^{3}2t$

Find the Laplace transform of the function $f\left(t\right)= \begin{cases} t, \\ 3, \end{cases} $ $0\leq t<2$ $t>2$