Two uniform, solid cylinders of radius R and total mass M are connectedalong their common axis by a short, light rod and rest on a horizontaltabletop. A frictionless ring at the rod’s center is attached toa spring of force constant k; the spring’s other end is fixed. The cylindersare pulled to the left a distance x, stretching the spring, then releasedfrom rest. Due to friction between the tabletop and the cylinders, the cylindersroll without slipping as they oscillate. Show that the motion of thecenter of mass of the cylinders is simple harmonic, and find its period.

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