The mass and stiffness matrices and the mode shapes of a two-degree-of-freedom system are given by

\[[m]=\left[\begin{array}{cc}m_{1} & 0 \\0 & m_{2}\end{array}\right], \quad[k]=\left[\begin{array}{cc}27 & -3 \\-3 & 3\end{array}\right], \quad \vec{X}^{(1)}=\left\{\begin{array}{l}1 \\1\end{array}\right\}, \quad \vec{X}^{(2)}=\left\{\begin{array}{c}-1 \\1\end{array}\right\}\]

If the first natural frequency is given by \(\omega_{1}=1.4142\), determine the masses \(m_{1}\) and \(m_{2}\) and the second natural frequency of the system.