Given the Transfer Function model of a second-order system as

\[\begin{equation*}H(s)=\frac{b}{s^{2}+a s+b}, \tag{3.33}\end{equation*}\]

(a) Calculate the per cent overshoot, settling time, peak time, rise time and pole locations for the following values: \(a=4\) and \(b=25\). Also, plot the poles.

(b) Repeat (a) for the another two sets of values: \(a=8\) and \(b=37 ; a=2\) and \(b=22\)

(c) Using MATLAB, plot the unit step responses of the three systems in one diagram.

(d) Compare the hand calculated and the experimentally determined (MATLAB) results for the following: overshoot, settling time, peak time and rise time for each of the three systems.