Problem $1$: Textbook Problem $8\mathrm{.}8$; Hint: Find damping ratio, $\backslash (\backslash$zeta $\backslash ).$ Small value of damping ratio $(\backslash (\backslash$zeta $\backslash ))$ implies larger number of oscillations.

$8\mathrm{.}8.$ The unit step responses of four second$-$order systems are shown in Figure P$8\mathrm{.}8,$ and four pairs of characteristic roots are listed below. Match each pair of roots with the corresponding step$-$response curve.