A disk with a mass M, a radius R, and a rotational inertia of I = 1⁄2 MR^2 is attached to a horizontal spring which has a spring constant of k as shown
in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk.
(a) Calculate the maximum translational velocity of the disk in terms of M,R, x, k.
(b) What would happen to the period of this motion if the spring constant of the spring increased? Justify your
© What would happen to the period of this motion if the surface was now frictionless and the disk was not allowed to roll? Justify your answer.