A light spring with spring constant k has one end attached to a wall and the other end connected to a block resting on a smooth horizontal surface. During a displacement, the work done by the spring is 1 2 kx^2 . The possible situations are

Step-by-step solution

The work done by the spring force is given by W = 1 2 kx_i^2 - 1 2 kx_f^2 , where x_i and x_f are the initial and final deformations (elongation or compression) of the spring from its natural length. Given that the work done by the spring is W = 1 2 kx^2 , we have: 1 2 kx_i^2 - 1 2 kx_f^2 = 1 2 kx^2 For the spring initially stretched by a distance x and finally returning to its natural length, x_i = x and x_f = 0 . Substituting these values, we get W = 1 2 kx^2 - 0 = 1 2 kx^2 . For the spring initially compressed b