2 The points \(A\) and \(B\) are at the same horizontal level a distance 4a apart. The ends of a light elastic string, of natural length \(4 a\) and modulus of elasticity \(\lambda\), are attached to \(A\) and \(B\). A particle \(P\) of mass \(m\) is attached to the midpoint of the string. The system is in equilibrium with \(P\) at a distance \(\frac { 3 } { 2 } a\) below \(M\), the midpoint of \(A B\).

1. Find \(\lambda\) in terms of \(m\) and \(g\).
   The particle \(P\) is pulled down vertically and released from rest at a distance \(\frac { 8 } { 3 } a\) below \(M\).
2. Find, in terms of \(a\) and \(g\), the speed of \(P\) as it passes through \(M\) in the subsequent motion.