Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum |
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| Authors: | Klaus Weltner Antonio Sergio C Esperidião and Paulo Miranda |
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| Institution: | (1) Universitaet Frankfurt, Fachbereich Physik, Institut fuer Didaktik der Physik Frankfurt, Graefstrasse 39, Germany |
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| Abstract: | We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-lineareffects. Firstly the natural frequency of a gravitational pendulum is measured as functionof its amplitude. Secondly forced oscillations of a gravitational pendulum are investigatedexperimentally without limiting amplitudes. By this arrangement new phenomena, thebistability and the jump-effect, can be observed. In the case of bistability the drivengravitational pendulum can oscillate in two different stable modes. Either it oscillateswith a small amplitude and approximately in phase with the exciting torque or it oscillateswith a larger amplitude and approximately anti-phase. The jump effect is the spontaneoustransition from one mode of oscillation to the other. Both effects can be demonstrated andexplained. |
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