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JEE Advanced 2013 Paper 2

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Question : 2

Total: 60

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 u0. When the speed of the particle is 0.5u0,it collies elastically with a rigid wall. After this collision :

the speed of the particle when it returns to its equilibrium position is u0
the time at which the particle passes through the equlibrium position for the first time is t=Π√
m
k
the time at which the maximum compression of the spring occurs is t=
4Π
3
√
m
k
the time at which the particle passes throughout the equilibrium position for the second time is t=
5Π
3
√
m
k

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