3. A particle \(P\) of mass \(m\) is attached to one end of a light elastic string, of natural length \(l\) and modulus of elasticity \(4 m g\). The other end of the string is attached to a fixed point \(O\) on a rough horizontal plane. The coefficient of friction between \(P\) and the plane is \(\frac { 2 } { 5 }\). The particle is held at a point \(A\) on the plane, where \(O A = \frac { 5 } { 4 } l\), and released from rest. The particle comes to rest at the point \(B\).

1. Show that \(O B < l\)
2. Find the distance \(O B\).