574 Coupled Vibrations by means of a Double Pendulum, 



system when the upper bob is displaced and the lower bob 

 free, and figs. 10 to 20 represent those of the system when 

 the lower bob is displaced and upper bob free. The figures 

 clearly show the effect of progressively increasing the 

 coupling ; the first figures, in which the coupling is loose, 

 show the phenomenon of beats. 



Thus the coupled system treated above presents an exact 

 mechanical analogy to the case of two mutually interacting 

 electrical circuits ; and at the same time it is much simpler, 

 and therefore a more convenient model by which the pro- 

 perties of the electrical case can be demonstrated to a class 

 or an audience. To a large audience it may be much better 

 demonstrated by allowing the reflected spots of light to 

 suffer another reflexion from a mirror rotating or oscillating 

 about a vertical axis and then projecting the spots either on 

 a screen or on a wall of the room. 



Withi a modified form of apparatus, experiments have been 

 carried out to illustrate the theory of three mutually inter- 

 acting oscillating circuits, and the mathematical theory of 

 the mechanical system " triple pendulum " is developed ; 

 and these results will be submitted for publication, shortly, 

 in another paper. 



Abstract. 



The author, following Prof. Lyle, Prof. Barton and 

 Miss Browning, and Mr. Jackson, describes an arrangement 

 of mechanical systems as an exact analogy of two magnetically 

 coupled circuits. 



The mathematical theory of the system is developed; and 

 the paper is accompanied by 20 photographic reproductions 

 of the simultaneous traces of the two pendulums, the method 

 adopted for photographing the vibrations being entirely 

 different from that adopted by the previous writers. 



At the same time, on account of its simplicity of arrange- 

 ment it is a very convenient model by which the properties 

 of electrical circuits can be easily demonstrated to a large 

 class to satisfy the non-mathematical student, who is often 

 mystified by the perfect silence of the high frequency 

 circuits. 



Department of Physics, 

 Maharajah's College, 



Vizianagaram City, India. 

 25th April, 1921. 



