Harmonic Oscillator Energy vs Angular Frequency

Mean energy of a harmonic oscillator in units of $k_\text{B}T$, against angular frequency $\omega = \sqrt{k/m}$ at fixed temperature. The oscillator is classical at low frequency and the ratio starts from its equipartition value, dips through a shallow minimum, then climbs linearly once $\hbar\omega$ outgrows $k_\text{B}T$ and the zero-point term $\hbar\omega/2$ dominates. Compare energy vs inverse temperature.