On the nonlinearity of a tuning fork

Tuning fork experiments at the undergraduate level usually only demonstrate a tuning fork's linear resonance. In this paper, we introduce an experiment that can be used to measure the nonlinear frequency response curve of a regular tuning fork. Using double-grating Doppler interferometry, we achieve measurement precision of the oscillation amplitude in the range of microns. With this experimental setup, we observe nonlinear behaviors of the tuning fork, such as the softening frequency response curve and the jump phenomenon. This provides an integrated experiment for intermediate-level students and a basis for senior research projects.