Modeling real-life pendula

ORAL

Abstract

Since being introduced into the theory of damped oscillations, we use linear differential equation to model various oscillating systems including a pendulum. But real world pendula are not linear systems (even when the amplitude of oscillations is small). For example, air drag on a real size pendulum (from a few cm to a few meters in length) is quadratic rather than linear (by velocity), and a friction in a pivot point is often dominated by a static (rather than velocity-dependant) term. As a consequence, the decay patterns of real pendula are usually different than a classic exponent. This can be often seen when students perform pendulum lab using computer interface. By including air drag, air viscosity and static friction into the equation of oscillations we obtained very realistic model of real pendula. A comparison of the results of such model with experiments are discussed in the presentation.

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Authors

  • Andrew Polemi

    Utah State University, Brigham Young University, University of Pennsylvania, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, High Altitude Observatory, University of Colorado at Boulder, Massachutes Institute of Technology, Utah Valley University, University of New Hampshire, Applied Physics Laboratory, Johns Hopkins University, University of Montana, Southwest Research Institute, University of Southern California, Lockheed Martin Advanced Technology Center, University of Chicago, Massachusetts Institute of Technology, SciPrint.org, Centre National de la Recherche Scientifique, Colorado State University, V. Alecsandri College, Bacau, Romania, Colorado School of Mines, National Renewable Energy Laboratory, Utah State University, Department of Physics, Brigham Young University, Provo, Huntsman Cancer Institute, Brigham Young University - Idaho, University of Arizona, Florida State University, Weber State University, Brigham Young University - Provo, New Mexico State University, Colorado State University, Fort Collins, CO 80523

  • Alexander Panin

    Utah Valley University