C.1.7—Qualitative energy changes in SHM

Describe one complete cycle

In ideal SHM, total mechanical energy is constant. As the particle moves from an extreme position to equilibrium, stored potential energy changes into kinetic energy; from equilibrium to the opposite extreme, kinetic energy changes back into potential energy.

Use quarter-cycle checkpoints

At an extreme, speed and kinetic energy are zero while the relevant potential energy is maximum. At equilibrium, speed and kinetic energy are maximum while that potential energy is minimum. The energy pattern repeats every cycle.

Connect the model

A circular-motion picture can help visualize phase: the projected coordinate oscillates between two extremes and passes equilibrium twice per cycle. Use it as a representation of the oscillation, while the energy explanation remains based on the SHM position and speed.

Common trap

Do not claim that the energy transfer stops at equilibrium. The particle has maximum speed there, so the transfer reverses direction as it continues toward the next extreme.