Question

One end of a light spring of spring constant $k$ is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is $+\left(\frac{1}{2}\right)k{x}^2$. The possible cases are:

• A. The spring was initially compressed by a distance $x$ and was finally in its natural length.
• B. It was initially stretched by a distance $x$ and finally was in its natural length.
• C. It was initially in its natural length and finally in a compressed position.
• D. It was initially in its natural length and finally in a stretched position.

Answer 1

Answer: (A), (B)

The spring was initially compressed by a distance $x$ and was finally in its natural length.
It was initially stretched by a distance $x$ and finally was in its natural length.

It is given that the work done by the spring force is positive.
Spring force is always towards mean position hence the displacement should also be towards the mean position.
So, the spring has to be in the compressed state first, for both the spring force and the displacement to be in the same direction.
Option A and B.