342 Prof. Barton and Miss Browning on a Syntonic 



logarithmic decrement per half period natural to the- 

 responders. 



Thus, for the indices of e in (2), we have 



k l t = k 1 {\ 1 /2v)-=S, 

 whence 



*,-?? (5) 



Referring again to equation (2) and using (4) and (5), we 

 may write for the amplitude of the forced vibration 



/ 



Y 1 = 



^/{(^-n"/ + (2A 1 n)»} 



Ai-f 



wwse-^i 



(6) 



and similar equations for Y 2 and Y 3 , the value of 8 being 

 assumed the same throughout. 



For the shape of the " resonance " curves we are concerned 

 only with relative responses, so may fitly take the ratio of Y 2 

 to its maximum value Y attained for l r = \ 1 . 



Then, from (6) we have 



Y — •' 



/V 



8ttv 2 S ' 



Thus £or the ordinate u x of the relative curves we have 

 _ Yj _ */X, 



(7> 



" 1= Y = 



Fig. 1. 



• . • (8) 



Resonance Curves. 



The three " resonance " curves shown by the full lines of 

 fig. 1 are plotted from equation (8) by giving u the three 



