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Department of Physics, Indiana University (HOM, June 1991)
Chaos Observed with a Buckled Beam
Goal:
Study of the onset of chaos in a simple, mechanical system. Acquaintance with strain gauges
as mechanical transducers.
Introduction
The study of chaos is a modern development in physics. It deals with the seemingly random
behavior of some phenomena in nature. It lead to the realization that some physical systems,
although perfectly deterministic in theory, exhibit a very complicated temporal development. This
complex behavior is also found in the math underlying these phenomena, thus the development of
computers played an important role in the study of chaos. Chaos can be found in many areas of
physics, including nuclear physics [BOH88].
The motion of an oscillator (with one degree of freedom, x) on which a periodic force acts
with frequency
ω
, is described by a secondorder differential equation
The second term describes damping. The restoring force g(x) can be taken as a polynomial with odd
powers of x. For the case where g(x)=
α
x, eq.1 describes a harmonic oscillator. In most cases, eq.1
has a simple, periodic solution, x(t), with a single frequency, that is, with a Fourier spectrum with a
single line. For some special choices of the coefficients in eq.1, however, x(t) becomes very
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 Fall '09

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