Set up the differential equations of motion for the double pendulum shown in Fig. 5.25, using the

Question:

Set up the differential equations of motion for the double pendulum shown in Fig. 5.25, using the coordinates $x_{1}$ and $x_{2}$ and assuming small amplitudes. Find the natural frequencies, the ratios of amplitudes, and the locations of nodes for the two modes of vibration when $m_{1}=m_{2}=m$ and $l_{1}=l_{2}=l$.

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