A block of mass m attached to an ideal spring of spring constant K is placed on a smooth horizontal surface between two fixed elastic walls AB and CD as shown. The block is at a distance d from CD and spring is in its natural position. The maximum velocity with which the block can be projected towards CD so that block performs complete SHM.

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Solution

The correct option is B

The SHM would be complete when the maximum displacement from mean position on either side is same. For maximum velocity to be imparted to block in above situation, the amplitude of oscillation must be d. Let V₀ is the required velocity then from work-energy theorem between initial instant and the instant when block just reached CD with zero velocity.

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