Nonlinear Oscillator

Posted on Feb 5, 2014

The purpose of this experiment is to discover the properties of a nonlinear circuit which closely approximates a driven pendulum. It`s a great introduction to nonlinear phenomena such as period doubling and chaos. `Chaotic States and Routes to Chaos in the Forced Pendulum, ` by D. D`Humieres, M. R. Beasley, B. A. Huberman, and A. Libchaber, Phys. Re

Nonlinear Oscillator
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v. A 26 3483 (1982). Our circuit is an improvement on theirs and is described in the section "Analysis of the Phase Locked Loop Circuit". Excerpts from Order Within Chaos by P. Berge, Y. Pomeau, and C. Vidal (Hermann and Wiley, Paris, 1984). This reference includes an introduction to the modem physics of dynamical systems. The following is a recommended sequence of steps for a long laboratory. Do not feel restricted to the operating parameters quoted in these notes, or even the methodology. Their main purpose is to help you get your feet wet. There is an enormous amount of investigation that can be done in this experiment, so feel free to focus on the parts you find most interesting, and also try out new ideas as they occur to you. Familiarize yourself with the TDS220 oscilloscope if you have not used one before. Learn how to view and scale traces, how to manipulate the trigger settings, and how to use the cursors. The scope also has useful functions under the "measure" menu. Look over the "Getting Started Guide" for the HP 35660A Dynamic Signal Analyzer. Look at the spectrum and the time series measurement for the signal source running as a sine wave, a periodic chirp, and a random noise source. Measure the frequency response of the low pass filter and the integrator modules of the oscillator. The procedure is described in Chapter 8 of the analyzer guide. Measure f0( = ‰0 / 2 ), the VCO frequency when the input is 0V (or...

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