QUARTZ CRYSTAL PLATES 



523 



as a system of coupled circuits.^- Consider the two coupled oscillatory 

 circuits shown in Fig. 5 having the uncoupled angular frequencies 

 coi and C02, then the frequencies of the coupled system in the absence 

 of damping will be given by the usual expression '^ 



_ VK"^!^ + <^2") ± WCi^r — ^r) + 4^''cora;2- 



k being the coupling. 



Vl - k"" 



(4) 



TUNING 



CIRCUIT NO. 2 



Fig. 6 — Angular frequencies of a system of two coupled circuits as a function of the 

 tuning of one circuit, the tuning of the other circuit being fixed. 



If these two frequencies be plotted as a function of the tuning of 

 the second circuit, i.e., C02, the familiar set of curves shown in Fig. 6 

 results. 



Suppose now other circuits are added to the system as shown in 

 Fig. 7, each additional circuit being fixed at a harmonic of the un- 

 coupled frequency of circuit No. 2, and so linked with this circuit 

 mechanically that the group is tuned as a whole. 



12 The term "circuit" is introduced here to describe a mechanical oscillatory 

 system because many readers are accustomed to think in terms of electrical circuits. 

 '^ See Pierce, "Elec. Osc. & Waves," Chap. VII. 



