1298 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



Combining equations (2) and (4) and solving for the acceleration, d), 



6(F^ - F.) + Fj ^ G- I<^ 



(d — nc) 2nr 



2Fmbnr 2iFsb - Fj)nr ., ^ . 



(d — nc) (d — fxc) 



or 



G 2FJ)txr , 2{Fsh - Fj)nr 



CO 



+ 



/„ /(i(f/ — nc) Iu((l — nc) 



Substituting the following values for F,„ , F^ , F 



F„, = mcoVo 

 Fs = mwlro 



then 



F = ^ 



2e 



G 2mw~rtthixr . 27ncoo'robur jurG 



oi = T — 1-n ^ + 



/o /o((i — ixc) Io{d — nc) Io{d — nc)e 



Substituting for the design constants 



K = To/r 



M = 2mr%K 



G Myoii , il/ucoo arjG 



0} = -7- — -i-n ^ + 



/o Io{d — lie) U{d — /ic) U{d — fic)e 



or 



. Mil 2 G , MiJL 2 nrjG .,. 



'^ + TTTt \ <^ = 7- + 7-7:1 v ''^o — 7-— ^ (5) 



io{d — lie) U Io{d — IXC) hid — iic)e 



This is of the form 



doi 2 7 



^ + SCO = A 



or 



dw 



h — g(xP- 



