**Answer:**

The potential energy of a spring increases when the spring is either compressed or stretched. This is explained by Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

When a spring is compressed or stretched, it is displaced from its equilibrium position. This displacement causes the spring to exert a restorative force in the opposite direction of the displacement. The magnitude of this force is given by the equation F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

Now, let's analyze the potential energy of the spring in different scenarios:

1. **When the spring is at equilibrium:**
- In this case, the spring is neither stretched nor compressed and is at its natural length.
- The displacement from the equilibrium position is zero (x = 0).
- Therefore, the potential energy of the spring is also zero since the force exerted by the spring is zero.

2. **When the spring is stretched:**
- If the spring is stretched, it is displaced in the positive direction from its equilibrium position.
- The displacement (x) is positive.
- The force exerted by the spring is in the negative direction.
- As the displacement increases, the magnitude of the force increases, resulting in an increase in potential energy.
- The potential energy of the spring is given by the equation U = (1/2) kx^2, where U is the potential energy, k is the spring constant, and x is the displacement.

3. **When the spring is compressed:**
- If the spring is compressed, it is displaced in the negative direction from its equilibrium position.
- The displacement (x) is negative.
- The force exerted by the spring is in the positive direction.
- As the displacement increases (in the negative direction), the magnitude of the force increases, resulting in an increase in potential energy.
- The potential energy of the spring is given by the equation U = (1/2) kx^2, where U is the potential energy, k is the spring constant, and x is the displacement.

Based on the above analysis, we can conclude that the potential energy of a spring increases when the spring is either compressed or stretched. Therefore, option D is the correct answer.

Potential energy of spring increases when there is a compression for depression in Spring .
and both have the same formula of potential energy,
U = 1/2(kx²)