Nonlinear Regime in Commercial Quartz Tuning Forks *

An essential part of any clock is a reference oscillator that precisely defines time. In electronics, the pendulum is performed by a quartz resonator. Often, these resonators are shaped as miniature tuning forks with resonant frequency of 2^15 Hz.



Doing frequency sweeps on a network-based spectrum analyzer; we found that commercial tuning forks can easily be driven to a nonlinear regime, where the frequency depends on the driving amplitude. This can be done at a driving amplitude as low as 10 mV and shifts about 300 millihertz. Resonance frequency depends on whether scans are from high to low frequency or low to high. The nonlinear regime is undesirable for clocks; other applications, such as sensors to detect physical quantities, may benefit. Many aspects of the nonlinear regime and the transition between regimes remain unclear. Our goal is to shed more light on the problem.

One way to illuminate the transition is to locate the tuning fork's bifurcation point. To find this point, we want to determine the coefficients of the Duffing equation for the forks. To solve this equation, atomic force microscopy is used to gain deeper insight into the nonlinearity phenomenon and map vibrations.

Part of this research was used to make a lab for undergrad students in lab.