3. A particle \(P\) of mass \(m\) is attached to one end of a light elastic string, of natural length \(a\) and modulus of elasticity 3.6 mg . The other end of the string is fixed at a point \(O\) on a rough horizontal table. The particle is projected along the surface of the table from \(O\) with speed \(\sqrt { } ( 2 a g )\). At its furthest point from \(O\), the particle is at the point \(A\), where \(O A = \frac { 4 } { 3 } a\).

1. Find, in terms of \(m , g\) and \(a\), the elastic energy stored in the string when \(P\) is at \(A\).
2. Using the work-energy principle, or otherwise, find the coefficient of friction between \(P\) and the table.