Mr. Milkovic’s two-stage oscillator as a parametric oscillator
Aleksandar B. Slavkovic
March 07, 2009
Pittsburgh, PA, USA
In this document I will show that Mr. Milkovic's two stage oscillator may be viewed as a damped parametric
oscillator, and that pumping of energy from the driving, swinging pendulum is not a precedent in the world of
physics, but rather, an expected effect due to a well-known phenomenon called parametric excitation, parametric
resonance or parametric pumping. Consequently, a ready-set of modeling tools should be applicable to properly
model the device.
A brief introduction to parametric resonance
Let it be sufficient to say that since 1883, when Lord Rayleigh published his paper "On maintained vibrations",
Philosophical Magazine, vol. 15, pages 229-235, a body of research has been produced on the topic of parametric
resonance. Ironically, most of it has been dealing with how to prevent instability in mechanical systems and
electric circuits. The latest research around parametric resonance is visible in many scientific disciplines, from
biology to quantum physics, pointing to the fact that parametric resonance is an often encountered and yet to
be fully understood and utilized natural phenomenon.
Now let’s review some well known definitions related to parametric resonance and oscillators. The statements in
items 1 through 4 are taken verbatim from Wikipedia’s pages on harmonic and parametric oscillators.
1. “A parametric oscillator is a simple harmonic oscillator whose parameters (its resonance frequency w and
damping ß) vary in time. Another intuitive way of understanding a parametric oscillator is as follows: a
parametric oscillator is a device that oscillates when one of its "parameters" (a physical entity, like capacitance) is
2. “Remarkably, if the parameters vary at roughly twice the natural frequency of the oscillator, the oscillator
phase-locks to the parametric variation and absorbs energy at a rate proportional to the energy it already has.
Without a compensat