Take the Laplace transform of the following initial value and solve for $Y(s) = \mathcal{L}\lbrace y(t) \rbrace$: $$y'' + {4} y= R(t) \hspace{0.5in} y(0)=0, \; y'(0)=0$$

Where $R(t) = \sin(\pi t) ,\hspace{0.2in} R(t+1) = R(t)$.

$Y(s)=$ .
Graph of $R(t)$ (a rectified sine wave function):