3. Two particles \(A\) and \(B\), of masses \(M \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively, are connected by a light inextensible string passing over a smooth fixed pulley. \(B\) is placed on a smooth horizontal table and \(A\) hangs freely, as shown. \(B\) is attached to a spring of natural length \(l \mathrm {~m}\) and modulus of elasticity \(\lambda \mathrm { N }\), whose other end is fixed to a vertical wall.
\includegraphics[max width=\textwidth, alt={}, center]{9699f53e-366b-4064-af9f-89992c5e93b7-1_333_405_1160_1572}
The system starts to move from rest when the string is taut and the spring neither extended nor compressed. \(A\) does not reach the ground, nor does \(B\) reach the pulley, during the motion.

1. Show that the maximum extension of the spring is \(\frac { 2 M g l } { \lambda } \mathrm {~m}\).
2. If \(M = 3 , m = 1.5\) and \(\lambda = 35 l\), find the speed of \(A\) when the extension in the spring is 0.5 m .