How is the elastic potential energy in a spring related to its displacement?

The elastic potential energy in a spring is directly proportional to its displacement.

When a spring is stretched or compressed, it stores potential energy in the form of elastic potential energy. This energy is stored due to the deformation of the spring from its equilibrium position. The amount of elastic potential energy stored in a spring is directly proportional to the amount of displacement from its equilibrium position. This can be expressed mathematically as:

Elastic potential energy = 1/2 kx^2

Where k is the spring constant and x is the displacement from the equilibrium position. This equation shows that as the displacement increases, the elastic potential energy stored in the spring also increases.

The relationship between elastic potential energy and displacement can also be seen in the graph of the spring's potential energy versus displacement. The graph is a parabolic curve, with the vertex at the equilibrium position. As the displacement increases, the curve becomes steeper, indicating a greater increase in potential energy.

In summary, the elastic potential energy in a spring is directly proportional to its displacement. This relationship is expressed mathematically and can be seen in the graph of the spring's potential energy versus displacement.