Two masses of 10 kg each are connected between fixed supports by outer springs of stiffness k=1250 N/m and a central spring of stiffness 2k, as shown. Find the higher natural angular frequency in rad/s (nearest integer).
The stiffness matrix is $K=k\begin{pmatrix}3&-2\\-2&3\end{pmatrix}$ and mass matrix is mI. In-phase motion has stiffness eigenvalue k and out-of-phase motion 5k. The higher frequency is $\sqrt{5k/m}=\sqrt{5(1250)/10}=25$ rad/s.
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