TELEPHONE DIAPHRAGMS. 



467 



the velocity x, at standard phase, by the angle az. The displacement 

 along OB2 is now more than 90° behind the impressed force. 



Consequently, as the angular velocity of constant impressed vmf, 

 increases from zero to infinity, the angular velocity co commences 

 at 90° lead with respect thereto, and indefinitely small magnitude, 

 later comes in phase, with maximum value, at the angular velocity of 

 resonance, or reactive equilibrium, and ends at 90° lag, again with 

 indefinitely small magnitude. 



In Figure 28, the line OX represents the value of r, the resistance 

 to motion, taken along the axis of reals. Xp is taken equal to the 



reactive diflFerence ; {vioo — -), drawn parallel to OY, the axis of 



CO 



imaginaries. The vector Oj), which may be called the mechanical 

 impedance, will make an angle a with OX, equal to the phase dis- 

 placement between the velocity and the impressed vmf. 



/ 



/ \ 



Fig. 28. Fig. 29. 



Locus OF Mechanical Impedance and Locus of Velocity under Varying 



Impressed Frequency. 



The equilibrium of vector forces represented in Figures 25, 26, and 

 27, for any steady state of angular velocity, may be expressed algebraic- 

 ally by the formula 



or 



sx — Tx — mx + / = 

 sx -{- rx -{- vix = f — Fe-'"' 



dynes Z (15) 

 dynes Z (16) 



