Abstract

Citation

Researchers should cite this work as follows:

• Reid, T. (2023). 2009-Reid-King-Pendulum Motion and Differential Equations. SIMIODE, QUBES Educational Resources. doi:10.25334/2X92-X458

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Article Context

Description

Reid, Thomas F.  and Stephen C. King. 2009. Pendulum Motion and Differential Equations. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies. 19(2): 205-217.

See https://www.tandfonline.com/doi/abs/10.1080/10511970701693942 . Accessed on 28 March 2023.

Abstract: A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect real-world behavior. We illustrate using linear and nonlinear restoring force assumptions for the pendulum model, comparing the model results with data from an actual pendulum.

A full presentation of equipment and procedures to collect data and model the pendulum device. While data is not presented the plot of the data is offered.

Keywords: differential equations, model, pendulum, data, analysis, parameter estimate, physical pendulum