472 KENNELLY AND AFFEL. 



respective vectors in Figures 26 and 31, the former being rotated at 

 the impressed angular velocity co, and the latter at the free angular 

 velocity oo^ The latter motion, however, speedily expires by damp- 

 ing, leaving the former in the steady state without further interference. 



Solution in Teems of Displacement. 



We have' hitherto considered only the solution of (15) in terms of 

 vibratory velocity^ a*. We may, however, find the solution in terms 

 of the displacement x, by integrating (17) as follows: 



1 \ F e^'"' 1 



icoj , Y 6-\ -A + jco' cm Z (31) 



r + J mo: ' 



CO 



\J03/ Z V^O / 



.i-A+j^')tyy cm Z (32) 



that is, the vector displacement of steady motion lags 90° in phase 

 behind the vector velocity, and is equal in magnitude to that velocity 

 divided by co. Also the vector displacement for transient motion 

 lags 180°-7° behind the vector velocity, and its magnitude is that 

 velocity divided by coq. 



All of the preceding theory is immediately applicable to the case of a 

 simple alternating-current circuit, containing resistance, inductance, 

 and capacitance in simple series, with an impressed sinusoidal emf. 

 when current strength i is substituted for velocity x, quantity q for 

 displacement x, inductance L for mass m, elastance S for elastic factor 

 s, and electric resistance R for mechanical resistance r. 



Applications of Simple Vibrator Theory to Telephone- 

 Receiver Characteristics. 



It can be shown ^^ that on the simple vibrator theory of telephone 

 diaphragm vibration, the vibromotive force may be expressed as 



/j = At instantaneous dynes (33) 



where f, is the alternating electromagnetic pull exerted on the equiv- 



21 Bibliography, No. 11. 



