586 Prof. T. E. Lyle on Mechanical Analogy to the 



which increases as the coupling is increased. Hence when 

 M is given the max. max. amp. of C 2 is obtained when the 

 tuning is done in accordance with the law 



T 2 = Tisec^, 

 after making the coupling sin -^ as close as is desirable. 



12. If initial conditions, different from those we have up 

 to the present assumed, be given to the motion, either of the 

 circuits or of the pendulums, different results will ensue, and 

 one case is sufficiently interesting to be briefly discussed 



here. 



When * = 0, let 



V l0 r 0! = E!, V 2 or 6 2 = E 2} 



d or 01=0, C 2 or 2 = O, 



that is, both condensers are charged or both pendulums are 

 deflected at the instant at which motion begins. 



Proceeding as in § 5, we find that the motion that ensues 

 is given by 



V ± or e i 



= lT{ ( s -a)E 1 +p 1 b'E 2 } cos ©!«+ {(*— ZOEx-jpi&Ea} cos co 2 tj, 



V 2 or 2 



pibcL 



w ith G 1 =K 1 DY 1} C 2 = K 2 DV 8 , 



all the symbols having the same significations as before. 

 Now if the initial P.D.s or deflexions be such that 



( 5 -a)E 1 +p 1 6E 3 = 0, 



the component whose frequency is ©! disappears, and the 

 resultant motion is a pure harmonic motion in both circuits 

 whose common frequency is a> 2 , the higher of the two 

 resultant frequencies of the system. In the pendulum 

 system this motion is unstable, and it is therefore probably 

 unstable in the coupled circuits. 



Again, if the initial values E : and E 2 be such that 



( 5 -c>)E 1 - j? > 1 &E 2 = 0, 



the component whose frequency is o» 2 disappears, and the 

 resultant motion is a pure harmonic motion in both circuits 



