Eigenvalues · Hard problem

A vibrating system has mass-normalized stiffness matrix $K = \begin{pmatrix}5 & -2\\-2 & 2\end{pmatrix}$, whose eigenvalues are the squares of its two natural angular frequencies. Find the period $T = \dfrac{2\pi}{\omega}$ of the FASTER normal mode (the one with the larger angular frequency $\omega$).