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4.11 Compute the natural frequencies and mode shapes of the following system: \left[\begin{array}{ll}

4 & 0 \\

0 & 1

\end{array}\right] \ddot{\mathbf{x}}(t)+10\left[\begin{array}{cc}

4 & -2 \\

-2 & 1

\end{array}\right] \mathbf{x}(t)=\mathbf{0} Calculate the response of the system to the initial conditions: Xo = [1 2] and vo= \left[\begin{array}{ll}

\sqrt{20} & -2 \sqrt{20}

\end{array}\right]^{T}

Fig: 1

Fig: 2

Fig: 3

Fig: 4