Using modal analysis, determine the free-vibration response of a two-degree-of-freedom system with equations of motion

\[2\left[\begin{array}{ll}1 & 0 \\0 & 1\end{array}\right] \ddot{\vec{x}}(t)+8\left[\begin{array}{rr}2 & -1 \\-1 & 2\end{array}\right] \vec{x}(t)=\overrightarrow{0}\]

with initial conditions

\[\vec{x}(0)=\left\{\begin{array}{l}1 \\0\end{array}\right\}, \quad \dot{\vec{x}}(0)=\left\{\begin{array}{l}0 \\1\end{array}\right\}\]