A light elastic spring has natural length \(l\) and modulus of elasticity \(4 m g\). A particle \(P\) of mass \(m\) is attached to one end of the spring. The other end of the spring is attached to a fixed point \(A\). The point \(B\) is vertically below \(A\) with \(A B = \frac { 7 } { 4 } l\). The particle \(P\) is released from rest at \(B\).
Show that \(P\) moves with simple harmonic motion with period \(\pi \sqrt { \frac { l } { g } }\)
Find, in terms of \(m , l\) and \(g\), the maximum kinetic energy of \(P\) during the motion.
Find the time within each complete oscillation for which the length of the spring is less than \(l\).