Linear Chaos in a Tape Recorder
A mathematical model of an analog tape recorder is developed and shown to exhibit linear chaos. The playback dynamics act as a wave and are modeled by a linear partial differential equation with a simple analytic solution. This linear dynamical system is shown to exhibit three properties commonly used to define chaotic dynamics: the solution set is dense with periodic orbits, contains transitive orbits, and exhibits extreme sensitivity to initial conditions. Thus, a tape recorder provides a common physical example of linear chaos.
The author recognizes Dr. Daniel Hahs, Dr. Shawn Pethel, and Dr. Shangbing Ai for helpful discussions regarding the interpretation and presentation of the research results.
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