Find normal frequencies and the forms of the normal modes

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A particle P of mass 3m is suspended from a fixed point O by a light inextensible string of length a. A second particle Q of mass m is in turn suspended from P by a second string of length a. The system moves in a vertical plane through O. Show that the linearised equations of motion for small oscillations near the downward vertical are

·· + Φ·· +4n2θ = 0,

θ·· + Φ·· + n2Φ = 0.

where θ and φ are the angles that the two strings make with the downward vertical, and n2 = g/a. Find the normal frequencies and the forms of the normal modes for this system.

Reference no: EM131384011

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