Conservation of mechanical energy applies to a simple harmonic motion system. The sum of the potential and kinetic energies is constant.

The total energy is equal to the maximum potential energy:

E = U_max = ½ kA²

It is also equal to the maximum kinetic energy:

E = K_max = ½ m v_max² = ½ mA² w²

Graphs of potential and kinetic energy as a function of time show that the total energy is constant, and that energies go through two complete cycles for each oscillation of the object.

The first set of graphs is for an angular frequency w = 1 rad/s. The second set of graphs is for w = 0.8 rad/s. This change of w is accomplished either by decreasing the spring constant or by increasing the mass. Which change did we make in this case?

1. We decreased the spring constant
2. We increased the mass
3. We could have done one or the other, you can't tell the difference

Graphing the energies as a function of position is also interesting.