17.2 Energy in simple harmonic motion

As an SHM oscillator moves, kinetic energy is greatest at equilibrium and elastic or other potential energy is greatest at the extremes; their sum is constant in the ideal model.

Use the position to infer the energy split and identify any damping or driving that would break constancy.

A spring mass has maximum elastic energy at x=±A and maximum kinetic energy at x=0.

Energy is not created at the centre; it has transferred from potential to kinetic.

For amplitude x₀ and angular frequency ω, total mechanical energy is E=½mω²x₀², equal to maximum kinetic or potential energy.

The formula assumes ideal SHM with no energy loss and uses amplitude, not instantaneous displacement.

Doubling amplitude quadruples total energy; doubling mass doubles it for fixed ω and amplitude.

Instantaneous kinetic energy is not always the total energy; it equals the total only at equilibrium.