A Note on Dynamics of a Swing

概要

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Sometimes the motion of a swing is explained as an example of parametric excitation phenomena where the spring stiffness in a vibrating system undergoes a periodic change with the frequency twice as much as the natural frequency of the system. This explanation is wrong, or at least insufficient in two points. The one point is that the parametric excitation in the case of swing motion is due not only to the periodic change of spring stiffness, but also to that of damping coefficient and the positive effect of the latter predominates over the negative one of the former. And the other point is that the motion of the driving person is usually with the frequency not twice as much as, but equal to the natural frequency of a pendulum composed of the swing and the driving person. These two points are clarified in this paper by considering the energy balance of swing driving with results retaining the essential features of swing motion as to the fundamental harmonic of the excited oscillation and within errors of small quantity of the 1st order.
山梨大学の論文