124 SYNCHRONOUS MOTORS 



If we let K equal the inertia of the motor, the period of oscillation 

 produced by this torque may be deduced by the known formula, 



2^2 



whence, on substituting, and noting that is nothing more than the 



short-circuit current, I sc , of one of the machines the motor closed on 

 hself, there remains 



<9 = - 



Ig C sin f cos 6 ' 



or, if we suppose 6 to be small enough so that cos may be taken as 

 equal to unity, we will have 



'--\f 



i) Vl 



KOJ 



sin f 



In the case where the machines are not similar and are running 

 at different speeds a\ and 2, it can be shown, in the same way (.4. 

 Blondel, loc. cit., p. 357), that the equation of oscillatory movement 

 is 





fi 



) 



In the case of small oscillations, if we replace the numerators by their 

 values, we have 



and assuming cos 0=i, and sin 6 negligible in comparison with cos 0, 

 we have 



whence 



