Harmonic Oscillator Energy vs inverse Temperature

Mean energy of a quantum harmonic oscillator in units of $\hbar\omega$, against inverse temperature $\beta = 1/k_\text{B}T$. As $\beta$ grows the thermal occupation dies off exponentially and the curve flattens onto $1/2$, the zero-point energy $\hbar\omega/2$ that survives at $T = 0$. Compare energy vs frequency.