The surface shown in the diagram are smooth and all collisions are elastic. Find the time period of the periodic motion.

Explanation

Before Ist collision, time speed `= (L)/(v)` after Ist collision, entire velocity is transferred to the second mass. This spring mass system covers half its oscillation before 2nd collision.
`therefore t = pi sqrt((m)/(K))` again velocity is transferred to the previous mass. It take `(L)/(v)` time again to reach its initial position
`therefore" "T = (2L)/(V) + pi sqrt((m)/(K))`