A light elastic string has natural length $0.6\text{ m}$ and modulus of elasticity $24\text{ N}$. One end is fixed at point $O$, and the other end is attached to a particle $P$ of mass $0.4\text{ kg}$, which is in equilibrium hanging vertically beneath $O$.
(i)[2]
Calculate the amount by which the string extends.
(ii)[4]
Particle $P$ is projected vertically downwards from the equilibrium position with speed $5\text{ m s}^{-1}$. Calculate the distance travelled by $P$ before it is first at instantaneous rest.
(iii)[4]
When $P$ is first at instantaneous rest, a stationary particle of mass $0.4\text{ kg}$ is attached to $P$. Find the maximum speed of the combined particle during the motion that follows.
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