- A particle \(P\) of mass \(m\) is attached to one end of a light elastic string of natural length \(a\) and modulus of elasticity \(3 m g\).
The other end of the string is attached to a fixed point \(O\) on a ceiling.
The particle hangs freely in equilibrium at a distance \(d\) vertically below \(O\).
- Show that \(d = \frac { 4 } { 3 } a\).
The point \(A\) is vertically below \(O\) such that \(O A = 2 a\).
The particle is held at rest at \(A\), then released and first comes to instantaneous rest at the point \(B\). - Find, in terms of \(g\), the acceleration of \(P\) immediately after it is released from rest.
- Find, in terms of \(g\) and \(a\), the maximum speed attained by \(P\) as it moves from \(A\) to \(B\).
- Find, in terms of \(a\), the distance \(O B\).