On resonant rotation of a weakly damped pendulum

The minimum, sinusoidal drive for resonant rotation of a weakly damped pendulum and the contiguous loci of stable states in a frequency-energy plane are determined by perturbing the solution for undamped, unforced oscillations and invoking the method of harmonic balance. Instability occurs through turning-point and period-doubling bifurcations, and the resonant states are stable only in rather small frequency intervals between these bifurcations.