A solid cylinder of mass M and radius R is mounted to an axle through its center. The axle is attached to a horizontal spring of constant k, as shown in the figure. Initially the cylinder is at rest and the spring is un-stretched. The cylinder is then pulled a distance A and released. The cylinder rolls back and forth without slipping.
A) Determine the angular frequency ωfreq and period T of the
B) Assume that we have the same spring and mass system, only
now the cylinder is released from rest on a frictionless surface at a distance A from the equilibrium position. What is the period of the simple harmonic motion of this system? Express your answer in terms of k and M.
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