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Model of a quartz crystal tuning fork using torsion spring at the joint of the arm and the base

We developed a method for analyzing the frequency of a quartz crystal tuning fork using torsion spring model. In order to calculate the frequency close to the actual frequency of the tuning fork, we approximated the right half of tuning fork to an L-shaped bar, of which two bars at both the base and the arm are in bending vibration. Furthermore, we applied torsion spring model with torsion spring constant R to the joint of beams A corresponding to the base and B corresponding to the arm. A comparison was made of frequencies calculated by this method with experimental results and the relation between R and the width of the base is discussed.