In Figure 15-57, a solid cylinder attached to a horizontal
spring (k = 9.50 N/m) rolls without slipping along a horizontal
surface. If the system is released from rest when the spring is
stretched by 0.340 m, find (a) the translational kinetic energy
and (b) the rotational kinetic energy of the cylinder as it
passes through the equilibrium position. (c) If the cylinder has
mass M = 3.50 kg, find the period of the simple harmonic motion
that the cylinder's center of mass executes. (Hint: Find the
time derivative of the total mechanical energy.)  Want an
answer?