A particle \(P\) of mass \(m\) is attached to one end of a light elastic spring of natural length \(a\) and modulus of elasticity \(5mg\). The other end of the spring is attached to a fixed point \(O\). The spring hangs vertically with \(P\) below \(O\).

The particle is pulled down vertically and released from rest when the length of the spring is \(\dfrac32a\).

Find the distance of \(P\) below \(O\) when \(P\) first comes to instantaneous rest.