108 DRIVING SYSTEMS 



IS ^ = ^r 



sin wt. The force, in dynes, between the plates is 



. _ (gp + gmax sin U>tY 



Im - g^^, 6.33 



^0^ + l^ot-max sin CO/ + l^^niax " l^^max COS 2co/ 



/m = ■ ^— -, 6.34 



The first and third terms in the numerator of equation 6.34 represent 

 steady forces. The fourth term is an alternating force of twice the fre- 

 quency of the impressed voltage. The second term is an alternating force 

 of the frequency of the impressed voltage. If the polarizing voltage e^ is 

 large compared to the alternating voltage f^ax sin wt the fourth term will 

 be negligible. The useful force, in dynes, then, is the second term which 

 causes the moving surface to vibrate with a velocity which corresponds to 

 the impressed voltage, 



gpgma x sin wt gpg 



where e = d'max sin wt. 



The motional impedance of this system will now be considered. 

 The charge, in statcoulombs, on the condenser is 



q = Cfi^o 6.36 



where e^ = potential difference between the plates, in statvolts, and 

 Ce = capacity per unit area, in statfarads. 



The current, in statamperes, generated due to motion is 



dt 

 From equations 6.36 and 6.37 the generated current is 



dCs dx 



t = eo — 6.38 



dx dt 



The capacity per unit area, in statfarads, is 



Ce = ~- 6.39 



\-KX 



The change in capacity with respect to a change in the spacing x is 



dCE _ 1 



dx 4x.Y^ 



6.40 



