[UPSC CSE 2003] Rigid Body Dynamics (Q231, 20M)

A block of mass m, attached to an ideal massless spring of force constant k, is at rest on a smooth horizontal floor. A second block of mass 2 m, moving with an initial velocity strikes the free end of the spring. The collision is one dimensional and elastic. (i) Calculate the maximum compression of the spring. (ii) What are the velocities of the block long time after the collision?