(Solved): Consider the following initial value problem:(a) Sketch the graph of the forcing function on an appr ...

Consider the following initial value problem: $y^{??}+4y=\sin t?u_{2z}(t)\sin (t?2?);y(0)=0,y^{?}(0)=0:$ (a) Sketch the graph of the forcing function on an appropriate interval. (b) Find the solution of the given initial valfiry problem. Indicale neparately the inalue of $\mathrm{e}$. $y(t)=$ where $c=$ (c) Ulie a graphing utility to view the graph of the solution, (d) Explain how the graphs of the forcing function and the solution are related. When the external force is on, the solution is periodic with a period and an amplitude When the coterinat force is removed, the solution