Analysis of quality factor of quartz-crystal tuning fork fabricated by etching process

We investigated a quality factor of the quartz-crystal tuning fork fabricated by the etching process. The center of gravity of two arms with the pentagonal configuration produced by the etching process is confirmed to be located on the same position of that with the rectangular configuration by our calculation. The calculated Q values for a cantilever beam with the deformed pentagonal section exactly coincide with that with the rectangular section of the arm when we analyze the equation of heat conduction including flexural influence for the arm with the rectangular section, not the pentagonal section.