A three degree-of-freedom undamped system has natural frequencies of (10 mathrm{rad} / mathrm{s}), (25 mathrm{rad} / mathrm{s}),

Question:

A three degree-of-freedom undamped system has natural frequencies of $10 \mathrm{rad} / \mathrm{s}$, $25 \mathrm{rad} / \mathrm{s}$, and $50 \mathrm{rad} / \mathrm{s}$. What are the differential equations satisfied by the principal coordinates for the system for free vibration?

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