Energy Conservation for Springs

When a mass attached to a horizontal spring oscillates on a frictionless surface, only the conservative spring force does work. Mechanical energy is conserved.

The total mechanical energy is the sum of elastic potential energy and kinetic energy:

Here $k$ is the spring constant, $x$ is the displacement from equilibrium, $m$ is the mass, and $v$ is the speed. Since the surface is frictionless and motion is horizontal, gravitational potential energy remains constant and we can ignore it.

This visualization shows how elastic potential energy and kinetic energy transform into each other while their sum remains constant throughout the oscillation.