Quantitative analysis of a smartphone pendulum beyond linear approximation: A lockdown practical homework

We present a detailed analysis of a smartphone pendulum, part of which was given as a homework assignment to first-year undergraduate students. We took care in the design and construction of the pendulum itself to draw maximum benefit from the high quality of the embedded sensors. Our students build a pendulum and analyze their data using the damped harmonic oscillator model. We introduce them to residue analysis to make them aware of slight nonlinearities in both the restoring and damping forces. Beyond what we ask our students, we present here results of numerical analyses to quantify these nonlinearities and demonstrate that aerodynamic drag contributes quite significantly to damping. We finally discuss our pedagogical experience using this assignment in the classroom.