@ Fig. 6.16 R (top view) 6.12. Another bead on a rotating hoop ** 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 w, about a given point (see Fig. 6.16). Find the equation of motion for the angle shown. Also, find the frequency of small oscillations about the equilibrium point.

@ Fig. 6.16 R (top view) 6.12. Another bead on a rotating hoop ** 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 w, about a given point (see Fig. 6.16). Find the equation of motion for the angle shown. Also, find the frequency of small oscillations about the equilibrium point.