1918] on Vibrations: Mechanical, Musical, and Electrical 21: 



phases. But when the forces alternate quicker than the pendukmi, 

 the latter swings almost in opposite phase. 



This change of phase of forced vibrations was illustrated by three 

 hanging pendulums all hanging from the same tightly stretched 

 horizontal cord. One pendulum had a heavy bob and by its swings 

 moved the stretched cord. It thus acted as driver and applied forces 

 to the other two pendulums which had light bobs and so were easily 

 driven. Of these pendulums one was shorter and one longer than 

 the driver. They soon settled to opposite phases after the heavy bob 

 was set in motion. Resonance curves showing the varied responses 

 of such driven pendulums as the tuning is altered were then shown 

 on the screen. 



In the cases just dealt with the light bolj is set in motion at the 

 expense of energy taken from the heavy one. But on account of 

 the great disparity of the bobs this loss entailed no appreciable 

 diminution in the vibrations of the heavy bob or driver. 



Consideration was next given to the case where equal bobs hang 

 from a tight cord. While both pendulums are hanging at rest one 

 bob is struck. Its vibrations disturb the other pendulum and set 

 it in motion. But obviously, while the driven pendulum gains an 

 amplitude equal to that first possessed by the driver, the driver itself 

 would have lost all its motion. The other then becomes the driver 

 in turn and transfers its energy back to what was originally the 

 driver. (Demonstration). 



This palpable surging of the energy to and fro between the two 

 pendulums marks them as showing what may be called coupled 

 vibrations. In both cases the action of the driver on the driven is 

 reco:;^nised. But in the case of coupled vibrations the reaction of 

 the driven on the driver is palpable and recognised also. Whereas 

 in what are called forced vibrations this reaction is undiscernible 

 or ignored. 



In the case of coupled vibrations just shown the vibrations of 

 each pendulum seem quite simple, but slowly and alternately wax and 

 wane in amplitude, that is, they exhibit what are termed " healsy 

 But it is well known that beats may be heard when two musical 

 tones of slight'y differing pitch are sounded together. Further, the 

 number of beats per second is the difference of the frequencies of 

 the two tones. Thus the waxing and waning vibrations of either 

 pendulum may be regarded as the superposition of two simple vibra- 

 tions of slightly different periods. 



The next case studied was that of two precisely similar pendulums 

 connected by hanging one from the bob of the other. One bob 

 l)eing started by a blow it appeared to execute simple vibrations. 

 The other moved with a pause or twitch instead of in simple fashion. 

 Further, neither pendulum showed the waxing and waning of ampli- 

 tude which was so marked in the other case where both hung from 

 -a stretched cord. 



YOL. XXII. (Xo. 11-2) s 



