Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum

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.