Many schools have recently transitioned to remote instruction to continue teaching during the COVID-19 pandemic. This presents a number of challenges for physics teachers, particularly those looking for remote physics laboratory options. One option is to teach students to use video analysis software (e.g., open-source Tracker1) to study mechanical systems with interesting dynamics that can be captured on video. One possible project is the parametrically pumped pendulum. There is a rich literature on this topic in The Physics Teacher and the American Journal of Physics that spans decades and relates topics as disparate as children swinging,2 the distribution of incense about a transept,3 and, by analogy, parametric resonance phenomena such as the orbit of particles in particle accelerators.4
Many physics experiments lend themselves to video analysis, but this particular experiment has the topical advantage of covering exponential growth: the maximum amplitude of the pumped pendulum...