﻿576 Vibrational Responders under Compound Forcing. 



frequency between those of the fifth and sixth responders 

 counting from the shortest (or in musical terms between 

 A|? and Gr). 



In fig. 6, on the contrary, the effect is due to starting the 

 pendulums simultaneously and in the same phase, so that 

 each swings with bridle and suspension remaining in a plane. 

 This isolates the slow motion of which the coupled pendulums 

 are capable, and the responders now show a maximum ampli- 

 tude at a frequency between D and D \>, to use the musical 

 terms. The longest responder, C, does not show in the 

 photograph. 



In PL IV. are seen the effects of starting one pendulum 

 while the other hangs free. This results in the quick and 

 slow vibrations being performed simultaneously by each 

 pendulum. Fig. 7 begins with about 10 per cent, coupling. 

 This leads to the execution of frequencies so near alike that 

 it is difficult to discriminate between them in the photograph. 

 The response is here seen to be spread upwards as compared 

 with fig. 6. In actually watching the responders, the beats 

 between the two rates of forcing were clearly visible. 



For a coupling of fifteen per cent., as shown in fig. 8, two 

 maxima are distinctly visible. Musically speaking, the 

 notes D and E are responding best, and the interval between 

 them is one tone. 



In passing from fig. 8 to 9, fig. 10 to 11, and fig. 11 to 12, 

 the position of the upper maxima rises by one responder at 

 a time, and it may be said musically that the pitch is raised 

 by a semitone each time. 



Between figs. 9 and 10 the pitch rises by a tone. Thus 

 in fig. 12 the responders called D and A will be found to be 

 the maxima, and the musical interval to be a perfect fifth. 

 The couplings required for the various responses are shown 

 on the Plate for each figure. 



In ordsr to show that the responders are responding 

 accurately to the two vibrations of the coupled pendulums, 

 traces might be taken on a board moving perpendicularly to 

 the pendulums. But as this has been done for the pendulums 

 alone, comparisons can be made between the figures on 

 PI. IV. of the 'present paper and Plate V. of " Vibrations 

 under Variable Couplings," Phil. Mag. vol.xxxiv. Oct. 1917. 

 It will be seen that fig. 12 of the present paper and fig. 7. of 

 the Oct. 1917 paper have the same coupling, and that the 

 ratio of the frequencies of the two component vibrations is 

 approximately 3 : 2 in each case, though exhibited in entirely 

 different ways. 



Nottingham, 



May 31, 1922. 



