Frequency Doubling In A Pendulum

A smartphone is used as a pendulum bob to simultaneously measure the angular velocity and the acceleration of a pendulum. The data show a frequency doubling in the radial acceleration component compared with the angular velocity and the azimuthal acceleration component. This is mainly due to the centrifugal force and is an illustration of frequency doubling in a simple mechanical system. This experiment might be used in first year university physics courses to teach frequency analysis and frequency doubling in a home laboratory.