From this expression, it is easy to see that for large values of formula_10, for very low temperatures, the average energy "U" in the Harmonic oscillator approaches zero very quickly, exponentially fast. The reason is that "kT" is the typical energy of random motion at temperature "T", and when this is smaller than formula_12, there is not enough energy to give the oscillator even one quantum of energy. So the oscillator stays in its ground state, storing next to no energy at all.