Phase plot of a gravity pendulum acquired via the MEMS gyroscope and magnetic field sensors of a smartphone

Abstract

A gravity pendulum experiment in which a smartphone serves as pendulum bob and as measurement device is described. As the pendulum oscillates, the smartphone gyroscope and magnetometer sensors are used to simultaneously record the bob's angular velocity and angular displacement. While the angular velocity is measured directly via the gyroscope sensor, the angular displacement is deduced from the change of the magnetometer reading while the smartphone oscillates in the constant magnetic field of the Earth. These two independent measurements enable us to derive the phase space representation of the pendulum motion directly from experimental data. Further data analysis yields energy plots, including the periodic change between the pendulum's kinetic and potential energy and the energy dissipation due to friction. Detailed instructions on how to adopt the experiment, which is both suitable as a lecture demonstration as well as an instructional laboratory experiment, are provided in the supplementary material.