Pendulum Motion and Differential Equations

摘要

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.