The spring constant is directly related to elastic potential energy.

The spring constant, represented by $k$, quantifies the stiffness of a spring. It is defined as the force required to either stretch or compress the spring by a specific distance. A larger spring constant indicates that the spring is more difficult to stretch or compress. Consequently, a spring with a higher spring constant will store more elastic potential energy compared to a spring with a lower spring constant when both are subjected to the same amount of displacement.

Elastic potential energy refers to the energy stored in an object when it is either stretched or compressed. This energy can be calculated using the formula:

where $E$ represents the elastic potential energy, $k$ is the spring constant, and $x$ is the displacement from the equilibrium position. This equation demonstrates that elastic potential energy is directly proportional to both the square of the displacement and the spring constant.

Thus, we can conclude that the spring constant is directly proportional to the elastic potential energy stored in a spring. A higher spring constant allows for more energy to be stored in the spring for the same degree of displacement, whereas a lower spring constant results in less energy storage. Understanding this relationship is crucial for various applications, including the design of springs for machinery and the calculation of energy stored in springs in physics problems.