Quartz tuning forks, such as those used in electronic watches etc., can be modeled mechanically as a damped, driven harmonic oscillator and electrically as a series RLC driven by an external voltage. The differential equations corresponding to these two models are of the same form with correspondances L Mass, R frictional loss coefficient, and 1/C spring constant. If the dimensions of the tines of the tuning fork are changed, the mass, the spring constant and hence the resonant frequency can be calculated easily. My question is whether the correspondance is strong enough that the changes in mass and spring constant can be used to calculate the changes in the motional inductance, L and the motional capacitance, C. For example, if the lengths of the tines of a tuning fork are doubled, the mass is doubled and the spring constant is reduced by 8, and the resonance frequency is reduced by a factor of 4. Have L and C increased by the corresponding factors of 2 and 8?

Any help including suggested references appreciated. I am trying to understand how changing the size of a quartz tuning fork would affect the performance for sensing forces such as in uses for atomic force microscopy.

thanks, Bret Cannon