Consider the free-vibration equations of an undamped two-degree-of-freedom system:

\[[m] \ddot{\vec{x}}+[k] \vec{x}=\overrightarrow{0}\]

with

\[[m]=\left[\begin{array}{ll}1 & 0 \\0 & 4\end{array}\right] \text { and }[k]=\left[\begin{array}{rr}8 & -2 \\-2 & 2\end{array}\right]\]

a. Find the orthonormal eigenvectors using the mass normalized stiffness matrix.

b. Determine the principal coordinates of the system and obtain the modal equations.