The following figure shows a homogeneous cylinder of radius R and mass m that is free to rotate about its axis of rotation and that is connected to the wall through a spring. Assuming that the cylinder rolls on a rough surface without sliding, and x and are measured from respective equilibrium positions, derive the equations of motion. Note that the moment of inertia J for the cylinder is equal to mR. (Use the law of conservation of energy) (30 points) k ellele 10 X