$4\mathrm{.}63.$ Consider the following two$-$degree$-$of$-$freedom system and

$\left[\begin{array}{cc}5& 0\\ 0& 1\end{array}\right]x^{}(t)+\left[\begin{array}{cc}20& -3\\ -3& 3\end{array}\right]x(t)=0,x_0=\left[\begin{array}{c}0\mathrm{.}1\\ 0\mathrm{.}05\end{array}\right],x_0^{}=0$; assume modal damping ratios of ${}_1=0\mathrm{.}01$ and ${}_2=0\mathrm{.}1$

a$)$ compute the response

b$)$ Plot the response. You may use Matlab.