A bead is free to slide along a frictionless hoop of radius r. The plane of the

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A bead is free to slide along a frictionless hoop of radius r. The plane of the hoop is horizontal, and the center of the hoop travels in a horizontal circle of radius R, with constant angular speed ?, about a given point (see Fig.). Find the equation of motion for the position of the bead. Also, find the frequency of small oscillations about the equilibrium point.image

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