The masses of the slender bar and the homogeneous disk are m and md respectively. The spri...

The masses of the slender bar and the homogeneous disk are m and md respectively. The spring is unstretched when θ = 0. Assume that the disk rolls on the horizontal surface.

(a) Show that the motion of the system is governed by the equation

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(b) If the system is in equilibrium at the angle θ = θe and  = θ – θ e, show that the equation governing small vibrations relative to the equilibrium position is

(See Example 21.2.)