A collar of mass m slides without friction along a circular track of radius R as shown in Figure P-5. Attached to the collar is a linear spring with spring constant K and unstretched length zero. The spring is attached at the fixed point A located a distance 2R from the center of the circle. Assuming no gravity and the initial conditions ?(t = 0) = ?0 and ? ?(t =0) = ? ? 0, determine
(a) the differential equation of motion for the col-lar in terms the angle ?
(b) the reaction force exerted by the track on the collar as a function of the angle ?