. The Bell System technical journal . e to resistance must he the samefor the plate at co,„ and for the electric circuit at w,i- This condition issatisfied if each is resonant at its ])articular fre(iuency, but resonance isnot a necessary condition. All that is necessary is that there be a pairof frequencies, whose sum is equal to that of the electric generator,for which the impedances have the same phase ant^le. If there are anelectric and a mechanical resonance such that the sum of the resonantfreciuencies is nearly equal to the generator frequency, and there is amarked difference in the sha
. The Bell System technical journal . e to resistance must he the samefor the plate at co,„ and for the electric circuit at w,i- This condition issatisfied if each is resonant at its ])articular fre(iuency, but resonance isnot a necessary condition. All that is necessary is that there be a pairof frequencies, whose sum is equal to that of the electric generator,for which the impedances have the same phase ant^le. If there are anelectric and a mechanical resonance such that the sum of the resonantfreciuencies is nearly equal to the generator frequency, and there is amarked difference in the sharpness of the two resonances, then theoscillations will fall closer to the sharper resonance. This is due to thefact that the phase angle of the impedance changes more rapidly withfrequency in the neighborhood of a sharp resonance. From (22) we see that the amplitude of the current at the generatorfrequency depends only on this frequency, the constants of the system,and the new frequencies. It is independent of the amplitude of the. 5 6 7 8 9 10 II 12 13IMPRESSED POTENTIAL (RMS) IN VOLTS Fig. 1—Alternating displacement of plate as a function of generator voltage. generator voltage, of the amplitudes of the new frequencies, and of theimpedance of the electric circuit at the generator frequency. Thisequation, while it tells us what happens when the oscillations arepresent, tells us nothing about the conditions for their are to be found by noting under what conditions the expression(23) for the amplitude at the new frequency, co^, is real. We have twocases to consider which are determined by the sign of cos {<pm + Zgig = ^ [Z,„a;„,,]i/2. (29) This shows th
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