EM-50 Chaotic Pendulum USB
EM-52 Chaotic Pendulum Upgrade
Components and software necessary to upgrade earlier Chaotic Pendulums for use with the USB input terminal of Wintel computers. The upgrade consists of the software, a driver box and the required cables. The driver box contains its own microcomputer with an accurate crystal for precise timing of the position measurements.
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The EM-50 Chaotic Pendulum provides a direct and accurate measurement
of Chaotic behavior in a real physical system. Developed by Professors James
A. Blackburn of Wilfred Laurier University and H.J.T. Smith of the University
of Waterloo, it exhibits a wide range of interesting dynamic modes not obtainable
in other mechanical, electrical or computer-based simulators.
The new design now uses the USB input of contemporary Wintel computers. It is compatible with Windows® 2000 and XP. |
The apparatus consists of a small 2 cm pendulum with ball bearing pivots driven by a sinusoidal torque of adjustable amplitude and frequency and damped by velocity-dependent eddy-currents. The position of the pendulum is read-out to ± 0.1° at a 50 kHz rate and plotted in real time on the computer screen. The drive frequency is read out to 0.001 Hz on a front panel display. The Drive amplitude is set by a second knob. The Drive can be disconnected if desired by a front panel switch.
The Phase Plane is a representation of the motion formed by plotting coordinate pairs angular position and angular velocity. The Poincaré plot has the same coordinates as the Phase Plane plot but is plotted each time the drive frequency passes through phase zero. If the motion is harmonic, the Poincaré plot will consist of a single repeating point.
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Non-driven swinging pendulum damping to rest
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Poincaré Plot of chaotic motion
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Chaos has no underlying periodicity, and each new point will be distinct from all others in the Phase Plane. Nevertheless, as points accumulate on a chaotic Poincaré map, a distinctive cloud-like pattern called "strange attractors" emerges.
The apparatus has a comprehensive Instruction Manual and a copy of Chaotic Dynamics, 2nd edition by G.L. Baker and J.P. Gollub that describes in detail the performance of this pendulum.