Two solid cylinders connected along their common axis by a short, light rod have radius R and

Question:

Two solid cylinders connected along their common axis by a short, light rod have radius R and total mass M and rest on a horizontal tabletop. A spring with force constant k has one end attached to a clamp and the other end attached to a frictionless at the center of mass of the cylinders (Fig. 13.38). The cylinders are pulled to the left a distance X, which stretches the spring, and released. There is sufficient friction between the tabletop and the cylinders for the cylinders to roll without slipping as they move back and forth on 1he end of the spring. Show that the motion of the center of mass of the cylinders is simple harmonic, and calculate its period in terms of M and k. [Hint: The motion is simple harmonic if a. and x are related by Eq. (13.8), and the period then is T = 2w/, Apply = I=u. and ~F, = Ma= c to the cylinders in order or relate a=., and the displacement x of the cylinders from their equilibrium position.]