304 Variably Coupled Vibrations. 



the experimental result is in good agreement with the theory. 

 Fig. 16 shows the effect of frequencies nearly 5:2; theory 

 indicates that for 65 per cent, coupling £>: q = 2'± : 1. 



Figs. 17-24 (Pl.YII.) are traces obtained when the upper 

 bob was displaced, the lower bob hanging free. A com- 

 parison with PL VI. brings out the dependence of the details 

 of the traces on the initial conditions. Thus fig. 20 (58 per 

 cent.) is a trace for the ratio p : q nearly equal to 2 : 1 ; but 

 the characteristic " kink " of the 2 : 1 curve is hardly visible, 

 low down in the troughs of the curve. Fig. 21 (58 per 

 cent.), on the other hand, shows the "kink" very well ; but 

 the trace is slightly distorted because the bob possessed, at 

 the time, a small transverse motion as well as the correct 

 longitudinal motion. Fig. 22 (approx. 59 per cent.) shows 

 the effect of a combination of frequencies rather greater than 

 2 : 1, producing a wandering of the "' kink," with a definite 

 period up and down the main curve. The figure shows 

 rather more than a complete cycle of this wandering. 



Figs. 25-32 (PL VII.) are traces obtained when the lower 

 bob was displaced, the upper bob being free. This was effected 

 by a horizontal thread, which was burnt when all was steady. 



The coupled system here described thus presents a fairly 

 close mechanical analogy to the case of coupled electric 

 circuits, as will be seen by the foregoing theory and experi- 

 ment. On account of the simplicity of the arrangement 

 it is a convenient model by the aid of which the somewhat 

 abstruse subject of coupled electrical vibrations can be 

 demonstrated to a class where visible results are needed 

 to satisfy the non-mathematical student. 



Summary. 



1. In the present paper the mathematical theory of a 

 coupled system consisting of a gravity and an elastic 

 pendulum is developed and confirmed experimentally. 



2. The paper is illustrated by 32 photographic repro- 

 ductions of the traces obtained for the motion of the lower 

 bob under various conditions of starting and coupling. 



3. The system here discussed gives very similar results to 

 those previously obtained with the Cord and Lath Pendulums 

 by Barton and Browning, and can be used as an analogy to the 

 electrical case of circuits of equal inductances and frequencies. 

 In this mechanical case, as in the electrical one, the motions 

 of the components of the systems are not interchangeable. 



4. It is hoped later to deal with the more general case of 

 the same arrangement in which both masses and periods are 

 unequal. 



Physical Department, 



University College, Nottingham, 

 June 1919. 



