A two SDOF has governing differential equations (left[begin{array}{ll}1 & 0 0 & 1end{array} ight]left[begin{array}{l}dot{x}_{1} dot{x}_{2}end{array}

A two SDOF has governing differential equations

\(\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}\right]+\left[\begin{array}{rr}5 & -2 \\ -2 & 2\end{array}\right]\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}\right]+\left[\begin{array}{rr}200 & -100 \\ -100 & 300\end{array}\right]\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}\right]=\left[\begin{array}{c}F(t) \\ 0\end{array}\right]\)

where \(F(t)\) is random with a power spectral density of \(S_{0}=5 \times 10^{-2} \mathrm{~N}^{2} \cdot \mathrm{s} / \mathrm{rad}\).

(a) Determine the mean square value of \(x_{1}\).

(b) Determine the mean square value of \(x_{2}\).