Problem $2(40$ points$)$

Does the following system decouple? If so$,$ calculate the mode shapes and write the equation in

decoupled form. $\left[\begin{array}{cc}3& 0\\ 0& 1\end{array}\right]x^{}(t)+\left[\begin{array}{cc}0\mathrm{.}9& -0\mathrm{.}1\\ -0\mathrm{.}1& 0\mathrm{.}1\end{array}\right]x^{}(t)+\left[\begin{array}{cc}9& -1\\ -1& 1\end{array}\right]x(t)=0$ for initial conditions

$x(0)={\left[\begin{array}{cc}0& 1\end{array}\right]}^{T}mm$ and $x^{}(0)=0mm.$ Compare the system physical response with the modal

coordinate response.