Two simple situations are considered ofNmutually coupled oscillators excited at resonance by external random sources. Formulas are derived for oscillator energies that display explicitly the transition from weak to strong coupling between the oscillators. Average oscillator energyE, the average uncoupled oscillator energyEu, and the coupled energyEcare defined. In one situation,E,Eu, andEcare equal; in the second situation,Eis bounded byEuandEc.