What is represented by the formula 1/2 kx²?

The formula ( \frac{1}{2} k x^2 ) represents elastic potential energy, which is the energy stored in an object when it is deformed, such as when a spring is compressed or stretched. In this formula, ( k ) is the spring constant, a measure of the stiffness of the spring, and ( x ) is the displacement from the spring's equilibrium position.

When an external force is applied to deform the spring, it stores energy proportional to the amount of deformation. As the spring returns to its original shape, this stored energy can be converted back into kinetic energy or work. Therefore, the relationship illustrated by the formula shows how potential energy is associated with the characteristics of elastic materials and their ability to return to their original form, confirming that this energy is termed elastic potential energy.

In contrast, gravitational potential energy relates to an object's height above a reference level, kinetic energy pertains to the energy of motion, and heat energy is associated with the thermal energy of particles. Each of these concepts describes different physical phenomena, hence differentiating them from elastic potential energy represented by the given formula.