4 A particle \(P\) of mass \(m\) is attached to one end of a light elastic string of natural length 4a. The other end of the string is attached to a fixed point \(O\). The particle rests in equilibrium at the point \(E\), vertically below \(O\), where \(O E = 5 a\). The particle is pulled down a vertical distance \(\frac { 1 } { 2 } a\) from \(E\) and released from rest. Show that the motion of \(P\) is simple harmonic and state the period of the motion. Find the two possible values of the distance \(O P\) when the speed of \(P\) is equal to one half of its maximum speed.