The Mercer online interactive chaotic pendulum

remotely control through the Internet. Our objective is threefold. We are attempting to provide an educational resource for chaos, demonstrate a new technology, and experiment with a new method of laboratory education. Figure 1 shows the pendulum control panel. As students vary the driving frequency, they can watch the pendulum's motion switch from simple periodic motion to chaotic motion. The control software incorporates several mathematical analysis functions so that students can view the pendulum data in different ways. Students can conduct experiments using the pendulum, download their data, and conduct their own mathematical analysis.signed the chaotic pendulum. TEL-Atomic (www.telatomic.com) markets a commercial version called the Multipurpose Chaotic Pendulum. (Details of the TEL-Atomic chaotic pendulum, as well as pendulums from several other companies, appear elsewhere. 1) We modified the commercial version to produce our online interactive version. A necessary condition for chaotic motion is that the bob can freely swing over the top. The bob is driven by an induction motor, with the pendulum arm connected directly to the motor ar-mature. An induction motor has little friction and is easily reversed by altering the phase of the drive coils. A square-wave drive signal (the black square wave in Figure 1) periodically reverses the motor's rotational direction. An eddy current sensor captures the velocity data. An aluminum disk connected to the motor shaft rotates between two rare-earth magnets mounted on a small cantilever. This rotation produces eddy currents, and the cantilever bends. A symmetric differential capac-itance sensor monitors the cantilever's deflection. Because the eddy currents are velocity dependent, the deflection indicates the velocity. We obtain position data by integrating the velocity signal, using a simple op-amp (LF 356) integrator circuit. Op-amp integrators use a capacitor for feedback and are prone to saturation. At DC (zero frequency), the capacitor blocks the feedback and the output wanders off to saturation. A common way around this problem is to make a " leaky " integrator, which places a high resistance across the capacitor. 2 However , this " hardware " integration produces an artifact in the phase space data. For periodic motion, the phase space plot should be a circle. The inte-grator circuit causes a slight phase shift, so the velocity and position signals are not exactly 90 degrees out of phase. Thus, the phase space plot appears elliptical. Software To perform remote control and data acquisition, we use National In-struments' (www.ni.com) LabVIEW, a graphical …