580 Prof. T. R. Lyle on Mechanical Analogy to the 



is -JKV 2 where K is the capacity and V the P.D. of the con- 

 denser. Hence the square of the amplitude of the condenser 

 P.D. at any time may be taken as proportional to the energy 

 in the circuit at that time. The analogous statement for the 

 pendulums is obvious. 



Let us consider the surging of the energy between two 

 coupled circuits (or coupled pendulums) that have been 

 tuned so that their natural frequencies are equal. 



Then a — b, s — a = s — b = ^ c, and the equations I. of § 5 

 giving the V's or 6'& become 



Y 1 = iE (COS (Qjt + COS C0 2 t) j 

 V 2 = JEa/^-2 (COS (Oit ~ COS C0 2 t) 



Pi 



where 



— = t>^ = t^ &>r the circuits, 

 Pi &2 Li 



= t for the pendulums. 



l 2 m 2 r 



These equations can be written as 



V ! = E cos -=-^ — t cos 2 1 1, 



9 



V, = E 



/p 2 . 0) 2 — (Oi /0) 2 + C0 li 7r\ 



A / 2 — sin tz — t cos ( -=— — - 1 — tt I 



V Pi 2 \ 2 2/' 



showing (1) that the amplitudes vary harmonically and have 



77" 



a constaut phase difference of - , that is, when one waxes 

 ihe other wanes ; (2) that the oscillations also have a con- 



7T 



stant phase difference of —, their frequency being J(e» 2 + co^ . 



From the values for a/ — given above it will be seen 

 that 



v Pl 



the amplitude of the amplitude or the maximum amplitude 

 of V 2 , is independent of the coupling when a = b, but that 



