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The response of a damped pendulum to a large driving force

Published online by Cambridge University Press:  01 April 1998

Michael Hinczewski  and
Joel C. W. Rogers
Michael Hinczewski
Affiliation:
Simon's Rock College of Bard, Great Barrington MA 01230, USA
Joel C. W. Rogers
Affiliation:
Simon's Rock College of Bard, Great Barrington MA 01230, USA
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Abstract

Analysing the motion of a driven, damped pendulum as a function of the amplitude of the driving force, we show, first, that for moderate values and larger of the amplitude, deviations from a simple motion with the period of the driving force are bounded by a constant times the inverse square root of the amplitude, for late times. For amplitudes above a larger threshold we are able to show that, for late times, the motion becomes a periodic motion with the period of the driving force. The manner in which this periodic motion is achieved with the passage of time is analysed.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 9 , Issue 2 , April 1998 , pp. 105 - 127
Copyright
Copyright © Cambridge University Press 1998

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