A GOVERNOR FOR TELEPHONE DIALS 1299 



Separating variables and integrating* 



t = -V Ln ^-- — + c where o" = - (0) 



2/1 q — CO g 



Applying the initial conditions to solve for the constant c 



CO = co(i at f = 



q ^ g + coo 



c = - -^ Ln 



2/1 g — ^too 



Substituting in etiuation (G) 



/ - '^ T ,. g+ ^ 9 T .. g + ^ o 

 f — —- Ijh — ~Y i^n 



2/i q — (ji 2h g — coo 



Letting 



Then 



q — m 



t = ^ Ln 1 ^^+^^ (7) 



2/1 .4 (q - co) ^^ 



and 



= q tanh f — + Ln y/A ) 



(8) 



Eciuation (8) applies as the equation of motion for the drive-bar 

 governor for speeds in excess of the critical speed when 



/o(rf — IXC) 



j^ ^ Gjd - (xc) + Mnwo^ - nrjG/e , . 



Io{d — nc) 



h ^ ^ /Gid - nc) + Mho' - nrjG/e ^^^ 



g V MfjL 



Appendix II 



GOVERNOR INPUT TORQUE 



In order to apply the theoretical speed eciuations and the chatter 

 equations de\'eloped for governors one must determine suitable values 



* Short Table of Integrals, Pierce, B. O., pp. 8, No. 50. 



