A spring of negligible mass, constant of restitution equal to k, and relaxation length equal to R is attached at one end to a horizontal hoop of radius R, while the other A small mass m is attached to the end and is constrained to move through the hoop. The The spring is initially stretched along the diameter of the hoop, with the mass at rest. The mass is pushed slightly, and it begins to move through the hoop as shown in the figure. figure. a) What is the normal force in the horizontal plane (that is, do not consider gravity) that the hoop exerts on the mass at the moment when it has traveled a quarter of its way around the hoop. b) Is there a point on the hoop at which the normal force it exerts on the mass is zero?

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