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 \(0.5 u_{0}\), it collides elastically with a rigid wall. After this collision :
1
the speed of the particle when it returns to its equilibrium position is \(u_{0}\)
2
the time at which the particle passes through the equilibrium position for the first time is \(\mathrm{t}=\pi\sqrt{\dfrac{\mathrm{m}}{\mathrm{k}}}\)
3
the time at which the maximum compression of the spring occurs is \(\mathrm{t}=\dfrac{4\pi}{3}\sqrt{\dfrac{\mathrm{m}}{\mathrm{k}}}\)
4
the time at which the particle passes through the equilibrium position for the second time is \(\mathrm{t}=\dfrac{5\pi}{3}\sqrt{\dfrac{\mathrm{m}}{\mathrm{k}}}\)