7 One end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N is attached to a fixed point \(O\). The other end of the string is attached to a particle \(P\) of mass 0.4 kg which hangs in equilibrium vertically below \(O\).

1. Calculate the extension of the string.
   \(P\) is projected vertically downwards from the equilibrium position with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Calculate the distance \(P\) travels before it is first at instantaneous rest.
   When \(P\) is first at instantaneous rest a stationary particle of mass 0.4 kg becomes attached to \(P\).
3. Find the greatest speed of the combined particle in the subsequent motion.