JEE Advanced 2013 Physics question

A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity . When the speed of the particle is , it collides elastically with a rigid wall. After this collision,

(A)the speed of the particle when it returns to its equilibrium position is .Correct
(B)the time at which the particle passes through the equilibrium position for the first time is .
(C)the time at which the maximum compression of the spring occurs is .
(D)the time at which the particle passes through the equilibrium position for the second time is .Correct

Answer: (A),(D)

Solution

Let ; . The speed becomes at , when the particle hits the wall. The elastic collision just reverses the velocity, so mechanical energy is conserved and the particle returns to equilibrium with speed (A true). After reversal it retraces its

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Question ID VK-026189