A resonance ω = k||v|| between energetic ions and a magnetic island with a half-width greater than the bulk ion Larmor radius is considered. As a result of such a resonant interaction, energetic ions with a relative density of a few per cent contribute significantly to the toroidal torque balance, leading to considerable modification of the equilibrium island rotation frequency ω. The possibility of a frequency pulsation scenario, instead of a stationary toroidal torque balance, is indicated.