The closed loop transfer function of a system is given by

\[
\mathrm{T}(s)=\frac{\mathrm{C}(s)}{\mathrm{R}(s)}=\frac{k(s+z)}{s^{2}+4 s+8}
\]

where \(k\) and \(z\) are adjustable.

(a) If \(r(t)=t\), find values of \(k\) and \(z\) so that steady state error is zero.

(b) For the values of \(k\) and \(z\) obtained in part (a), find \(e(\infty)\) for input \(r(t)=\frac{1}{2} t^{2}\).