Answer :

When the block A moves with the velocity v and collides with the block B, it transfers all energy to the block B (elastic collision). The block A will move a distance x against a spring, again the block B will return to the original point and completes half of the oscillations.

So, the time period of B is



The block collides with the block A and comes to rest at that point. The block A moves a further distance


L to return to its original position.


Therefore, time taken by the block to move from MN and NM is


Hence time period of the periodic motion is


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