Calculate elastic potential energy from spring constant and extension.

Elastic potential energy is the energy stored in an elastic object when it is stretched or compressed. This energy can be calculated using the formula: elastic potential energy = 0.5 x spring constant x extension squared. Here, the spring constant measures the stiffness of the spring, while the extension is the change in length from its original position. It's important to note that the relationship between extension and elastic potential energy is not linear; doubling the extension results in more than double the elastic potential energy due to the squared term in the equation. This principle is crucial in understanding how elastic materials behave under force.