A particle is attached to one end of a light inextensible string of length \(l\). The other end of
A light elastic spring, of natural length \(5 a\) and modulus of elasticity 10 mg , has one end attached to a fixed point \(A\) on a ceiling. A particle \(P\) of mass \(2 m\) is attached to the other end of the spring and \(P\) hangs freely in equilibrium at the point \(O\).
Find the distance \(A O\).
(3)
The particle is now pulled vertically downwards a distance \(\frac { 1 } { 2 } a\) from \(O\) and released from rest.
Show that \(P\) moves with simple harmonic motion.