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 `u_0`. when the speed of the particle is `0.5u_0`, it collides elastically with a rigid wall. After this collision

Options

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 =`pisqrt((m)/(k))`
C. the time at which the maximum compression of the spring occurs is` t=(4pi)/(3) sqrt((m)/(k))`
D. the time at which the particle passes through the equilibrium position for the second time is
`t= (5pi)/(3) sqrt((m)/(k)) `

Answer

A, D