Abstract
The dynamically shifted oscillator is a nonlinear system described by a differential equation of motion which includes a Hooke's law restoring force plus a stiffness force which depends only upon the sign of the displacement. The natural frequency of the oscillator is a function of the displacement amplitude; for positive stiffness it increases as the amplitude decreases. Because of the special nature of the nonlinearity it is possible to find an exact expression for the displacement waveform as a function of time. In the limits of zero Hookian force or zero stiffness, the waveform becomes, respectively, a cosine wave or a parabola wave. Conservation of energy leads to an integral equation which can be solved to find an exact expression for the amplitude‐dependent frequency. If the model equation is extended to include damping then the model predicts the time dependence of the frequency. The latter is compared with the measured time‐dependent frequencies of two systems to which the dynamically shifted oscillator theory can be applied, the spring doorstop and the two‐point librator.
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