a$)(3$ pts$)$ Using Laplace transform solve for $)$ in problem B$-2-23$ in your textbook $($System

Dynamics, Ogata, $4^{th}$ edition$).$ Please show all the steps in your solution.

b$)(1$ pt$)$ Using the Initial Value Theorem $($IVT$)$ and Final Value Theorem $($FVT$),$ find the initial value

and final value $(x_{ss})$ of $x(t).$ Use ${}_n=0\mathrm{.}5ra\frac{d}{s}.$

Hint: IVT$=\underset{s}{lim}sx(s)$ and $FVT=\underset{s0}{lim}sx(s)$

c$)(1$ pt$)$ Using Matlab, for the frequency ${}_n=0\mathrm{.}5ra\frac{d}{s},$ plot $x(t).$ What is the IV and FV from the

plot?