M. Hinczewski et Jcw. Rogers, THE RESPONSE OF A DAMPED PENDULUM TO A LARGE DRIVING-FORCE, European journal of applied mathematics, 9, 1998, pp. 105-127
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.