A 50-cmcm-long spring is suspended from the ceiling. A 310 ggmass is connected to the end and held at rest with the spring unstretched. The mass is released and falls, stretching the spring by 28 cmcmbefore coming to rest at its lowest point. It then continues to oscillate vertically.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.