Two uniform, solid cylinders of radius r and total mass m are connected along their common axis by a short, light rod and rest on a horizontal tabletop (figure 1). A frictionless ring at the rod's center is attached to a spring of force constant k; the spring's other end is fixed. The cylinders are pulled to the left a distance x, stretching the spring, then released from rest. Due to friction between the tabletop and the cylinders, the cylinders roll without slipping as they oscillate. Show that the motion of the center of mass of the cylinders is simple harmonic, and find its period.

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Alex is the head photographer for the yearbook and the newspaper. she has a large staff of assistant photographers because they need to take pictures at all of the school events. she knows that some of her photographers have better cameras and can take action shots at sporting events, and that some of them are good at taking candid pictures in the hallways. she sets firm deadlines so she has enough time to look through all of the shots and choose the best ones. she gives her photographers constructive feedback to them improve their pictures. respectful enforcer warlord doormat peacemaker

Rick is on a bicycle trip. every 4 days he bikes 230 km. if rick keeps this same pace for 16 days, how many kilometers will he bike?