Coupled Circuits used in Wireless Telegraphy. 

 which, when damping is neglected, reduces to 



{ 





)* 



= 0. 



569 



(IV.) 



M/ VL1L2, usually spoken o£ as the coefficient o£ coupling, 

 or the coupling, of the two circuits will be represented in 

 what follows by sini/r, and i/rwill be called the coupling 

 angle, so that 



M 2 



sin 2 i/r = r T . 



IjiL/2 



3. Consider now the motion of the following mechanical 

 system when making small oscillations. 



A horizontal beam of mass M is so supported that it can 

 move freely in the direction of its length, and from it two 

 simple pendulums of lengths l x and l 2 with bobs of masses 

 m 1 and m 2 are suspended by means of V suspensions so 

 arranged that the bobs are constrained to move in the vertical 

 plane through the axis of the beam (see fig. 1). 



Fiff. 1. 



e 



3 



Let the position of the beam be specified by x, the hori- 

 zontal distance between its end and a fixed origin, and that 

 of the pendulums by 1 and # 2 > the angles they make with 

 the vertical, ± being measured towards the left and 6 2 

 towards the right ; then if T be the kinetic and V the 

 potential energy of the system when making small oscillations, 



2T = MP + m-^x - I A) 2 + m 2 (x + l 2 6 2 f 

 2V=g{m 1 l 1 1 * + m 2 l 2 2 *), 



and as 



d dT dV 



