The differential equations of motion for a two-degree-of-freedom system are given by [begin{aligned}& a_{1} ddot{x}_{1}+b_{1} x_{1}+c_{1} x_{2}=0

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The differential equations of motion for a two-degree-of-freedom system are given by

\[\begin{aligned}& a_{1} \ddot{x}_{1}+b_{1} x_{1}+c_{1} x_{2}=0 \\& a_{2} \ddot{x}_{2}+b_{2} x_{1}+c_{2} x_{2}=0\end{aligned}\]

Derive the condition to be satisfied for the system to be degenerate.

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