One end of a light elastic spring, of natural length \(a\) and modulus of elasticity 5 mg , is attached to a fixed point \(A\). The other end of the spring is attached to a particle \(P\) of mass \(m\). The spring hangs with \(P\) vertically below \(A\). The particle \(P\) is released from rest in the position where the extension of the spring is \(\frac{1}{2} a\).
(a) Show that the initial acceleration of \(P\) is \(\frac{3}{2} g\) upwards.
(b) Find the speed of \(P\) when the spring first returns to its natural length.