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WORKSHEET periodic motion NAME A cart of mass m on a linear track is attached to the ceiling, a distance L above, by a spring of spring constant k. The cart oscillates back and forth periodically along the x axis. The spring has un-stretched length L. Ignore any damping forces. 5" (a) Show that when the cart is at position x, the x-component of L the force on the cart is l (b) Lots of systems exhibit periodic motion that is not exactly SHM, but is approximately SHM for small oscillations. (The pendulum is an example.) Use the binomial expansion to approximate the force for the contraption above, for x/ L l . If the approximated force is proportional to mx, then the motion is SHM, for small oscillations. Is it? (c) Now suppose there is a small coefcient of kinetic friction between the cart and track. Where is the friction force greatest, or is it uniform? Explain