PROCEEDINGS OF SECTION A. 



27 



Mj ^L\L%, usually spoken of as the co-effioient of coupling, or the 

 coupling of the two circuits will be represented in what follows by sin »// 

 and -^ will be called the coupling angle, so that sin^ ^ = M^lLxLi. 



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\ and Iz with bobs of masses mi and m^ 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. I). 



M 



Fig I. 



Let the position of the beam be specified by a;, the horizontal 

 distance between its end and a fixed origin, and that of the pendulums 

 by 01 and 02, the angles they make with the vertical, 0i being 

 measured towards the left and 02 towards the right ; then if T be the 

 kinetic, and F the potential energy of the system when making small 

 oscillations, 



and as 



2T = Mx^ + mx{x-lxQ\f + mt{x + h^t)' 

 2V = gimikOi^ + m2l20i^) 



d dT 



_. — + 



dV 

 d<p 



= 



^^ 



« •» 



•ftX 



•v^/ 



