Parametric Resonance in a Linear Oscillator

The phenomenon of parametric resonance in a linear system arising from a periodic modulation of its parameter is investigated both analytically and with the help of a computer simulation based on the educational software package PHYSICS OF OSCILLATIONS (see in the web http://www.aip.org/pas). The simulation experiments aid greatly an understanding of basic principles and peculiarities of parametric excitation and complement the analytical study of the subject in a manner that is mutually reinforcing. The parametric excitation is studied on the example of the rotary oscillations of a mechanical torsion spring pendulum caused by periodic variations of its moment of inertia. Conditions and characteristics of parametric resonance and of parametric regeneration are discussed in detail. Ranges of frequencies within which parametric excitation is possible are determined. Stationary oscillations on the boundaries of these ranges are investigated.