An Experimental Investigation of Forced Vibrations in a Mechanical System Having a Non-Linear Restoring Force

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Abstract
This paper introduces a mechanical apparatus capable of generating and recording forced vibrations in a system having a non‐linear restoring force. The experimental wave forms are then compared with the theoretical results given by three graphical methods. These are the methods of Martienssen, Hartog, and Rauscher. Provided a suitable first guess for the amplitude can be made, one application of Rauscher's method gives better results than the other methods. A graph is made of the experimental amplitude as a function of the disturbing frequency. These results are compared with the theoretical results of the above three methods. Again one application of Rauscher's method gives satisfactory results. In all experimental results it is noted that even though the restoring force is distinctly non‐linear, the wave forms of the resulting motion are nearly sinusoidal as long as the frequency of the observed motion is the same as the frequency of the disturbing force. However, steady oscillations can be maintained for which the observed frequency is a sub‐multiple of the disturbing frequency. Two such subharmonics were recorded and the experimental wave forms are shown.

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