Question

A body of mass $m$ hangs by an inextensible string that passes over a smooth mass less pulley that is fitted with a light spring of stiffness $k$ as shown in the figure. If the body is released from rest and the spring is relaxed, find the maximum elongation of the spring.

Answer 1

In this situation body oscillate about mean position.

At mean position, tension $T=mg$

$kx=2T=2mg$

$x=\frac{2mg}{k}$

So maximum elongating in the spring is $=2x=\frac{4mg}{k}$