Three beads of mass m, m, and 2m are constrained to slide along a frictionless, circular h...

Three beads of mass m, m, and 2m are constrained to slide along a frictionless, circular hoop. The two small masses are each connected to the large mass and to each other by springs of length a and force constants k and k', respectively. The masses are Shown in Figure at their equilibrium positions, which are located at 120° angular separations. The largest mass is initially displaced 10° clockwise from its equilibrium position, and the other two are held fixed in place. The three masses are then simultaneously released from rest.

(a) Find the normal frequencies and normal modes of oscillation.

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(b) Solve for the resulting motion of each mass.

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