A bead of mass in slides without friction on a fixed vertical hoop of radius R. The bead moves under the combined action of gravity and a spring with spring constant k. The spring is attached to the bottom of the hoop. For simplicity, assume that the equilibrium length of the spring is zero. The bead is released from rest at with a non-zero but negligible speed to the right. The gravitational acceleration g is directed downward in the figure below. Express your answer to the following questions in terms of some or all of the parameters m. R. k and g.
(Part a) What is the speed v of the bead when ?
(Part b) What is the magnitude of the force that the ring exerts on the bead when ?
