Example $7\mathrm{.}12$ : The transfer function of a second$-$order system is given by:

$G(s)=\frac{(\frac{?}{\text{b}\text{a}\text{r}}(y))(s)}{(\frac{?}{\text{b}\text{a}\text{r}}(f))(s)}=\frac{1}{p{s}^2+qs+r}$

The input variable $F(t)$ is given step change of $8$ units, which cause the output $y(t)$ to approach steady$-$state ultimate response of $0\mathrm{.}5$ units as shown in Fig. $7\mathrm{.}48.$

Find the values of $p,q$ and $r.$