Nonlinear tuning curves of a tuning fork

Cantilever beams of a tuning fork have both hardening and softening oscillation modes. Yet, teaching experiments concerning tuning forks usually only demonstrate their linear resonance. In this work, we introduce a simple experiment that can be used to measure the nonlinear tuning curve of a regular tuning fork. Using double-grating Doppler interferometry, our measurement accuracy reaches tens of micron. With this experimental setup, we observed typical nonlinear phenomena of the tuning fork such as the bent tuning curve and "jump phenomena". Our experiment is inexpensive and easy to operate, so it can readily be used as a lecture demonstration for undergraduate students.