Question

Select One Option Correct from the following : A particle of mass m is attached to one end of a massless 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 t = 0 with an initial velocity $u_0$. When the speed of the particle is $0.5u_0$, it collides elastically with a rigid wall. After this collision,
(A)the speed of the particle when it returns to its equilibrium position is $u_0$ .
(B)the time at which the particle passes through the equilibrium position for the first time is $t=\pi\sqrt{\frac{m}{k} }$ .
(C)the time at which the maximum compression of the spring occurs is $t=\frac{4 \pi}{3}\sqrt{\frac{m}{k} }$ .
(D)the time at which the particle passes through the equilibrium position for the second time is $t=\frac{5 \pi}{3}\sqrt{\frac{m}{k} }$.

Answer 1

d is correct I think.

Answer 2

(D)the time at which the particle passes through the equilibrium position for the second time is $t=\frac{5 \pi}{3}\sqrt{\frac{m}{k} }$.