Abstract

Students know that a simple harmonic oscillator (SHO) has a ‘resonance curve’, and some students even know how to label the axes of a plot showing that resonance curve. The frequency (and amplitude) of a sinusoidal drive force are the main independent variables, and the steady-state amplitude of the SHO’s response is the main dependent variable. But a simple modification to a mechanical SHO can change it from ‘direct drive’ to ‘parametric drive’, and this subtle change has dramatic consequences. First of all, parametric resonance occurs when the drive frequency is not at the SHO’s natural frequency, but nearly _double_ that frequency. Next, there no longer emerges any steady-state amplitude of response, and the right dependent variable to measure is the rate of _exponential growth_ (or decay) of the system’s oscillations. There is also a _threshold amplitude_ for the drive required to give any growth in the response. This presentation features a torsional SHO with a non-contact parametric drive, and shows theoretical predictions and experimental data for its performance. Finally, we connect this parametric drive of a mechanical SHO to some glamorous applications of parametric excitation in modern physics.

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