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

 where <$> is any one of the coordinates, we find that 

 (M + m^ + m 2 )x — mil 1 l + m 2 l 2 6 2 = 



x + l 2 O 2 +g0 2 = 0. 



Eliminating x from the first and second, and also from the 

 first and third of these equations, we obtain 



(D 2 + / v)0 1 =- Pl D 2 <? i n 



and \ . . . (I.) 



(D , +Mi , )0,= -M^iJ 

 wher 



*e 



2 _M. + m 1 + m 2 g 2 __M + m 1 + m 2 g "] 



^ " M + m 2 r t ' ^ " M + 7% V I 



/ / ' ^ (IL) 



_ t 2 m 2 li nil 



Pl ~r i M + m 2 ^ ^ 3 = / 2 M + ?n 1 " 



Equations II., § 2, connecting the P.D.s of the condensers 

 in the coupled circuits can, when damping is neglected, be 

 written in the identical form of equations I. of this para- 

 graph, and the values of the constants for the electrical case 

 are given by 



(in.) 



Hence the angular displacements of the two pendulums 

 in the mechanical system are mutually connected by equa- 

 tions identical inform with those which connect the P.D.s of 

 the condensers in the electrical system, and as Ci = K 1 DVi, 

 C 2 = K 2 DV 2 , the angular velocities of the pendulums are 

 similarly analogous to the currents in the two electrical 

 circuits. 



If in the proposed system the strings of the second 

 pendulum become rigid and be rigidly attached to the beam, 

 then D 2 # 2 = 0, and the equation of motion of the first 

 pendulum becomes 



(D' + ^-^O, 



that is, the motion is simple harmonic of frequency yu-j. 



Hence, to determine the quantity relating to the mechanical 



2 1 



1 

 1X2 ~ K 2 L 2 ' 



1 

 1 



y 

 \ 



j 



K 2 M 



K, M 



P2- K 2 V 



