THE RESPONSE OF A DAMPED PENDULUM TO A LARGE DRIVING-FORCE

Analysing the motion of a driven, damped pendulum as a function of the amplitude of the driving force, we show, first, that for moderate val ues and larger of the amplitude, deviations from a simple motion with the period of the driving force are bounded by a constant times the in verse square root of the amplitude, for late times. For amplitudes abo ve a larger threshold we are able to show that, for late times, the mo tion becomes a periodic motion with the period of the driving force. T he manner in which this periodic motion is achieved with the passage o f time is analysed.