Assuming small amplitudes set up the differential equations, Ask an Expert

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Assuming small amplitudes, set up the differential equations of motion for the double pendulum using the coordinates shown in Figure.

Show that the natural frequencies of the system are given by the equation

ω=[√(g/t)(2±√2)]

Determine the ratio of amplitudes X₁/X₂ and locate the nodes for the two modes of vibration.

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