It is shown that for a collection of n classical harmonic oscillators, the long-time distribution of potential energies P is approximated by sin(m)(pi P) for n greater than or equal to 4, where m=(8n/pi(2)-1/root 2) and P is scaled to lie between 0 and 1. As n-->infinity, the distribution tends to a delta-function centered about P=0.5. When coupling is present between the oscillators, the effective value of m is reduced, so that the breadth of the potential energy distribution reflects the degree of randomization in the system.