17.2.2—E = 1/2 mω2x0 2 for the total energy of a system undergoing simple harmonic

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.