﻿490 Dr. J. H. Vincent and Mr. 0. W. Jude on 



Index of Diagrams 1 to 18. 



-^ ! Frequencies I Pendulum! 

 as ! at rest. 



18 



\% 3,4, 5 



}• 1,2, 3,4 



Initial conditions 

 ^amplitudes all a). 



Displacements all negative. 



Ail negative except A. 



All negative except B. 



A and B positive, C and D negative. 

 D releases C, C releases B. 

 B releases A when each has com- 

 pleted a quarter of a vibration. 



D releases B, B releases A and C at 

 once as above. 



i All starting 

 together. 



All start 

 from nega- 

 tive position. 



Frequencies as 2 } 3, 4, 5. 



The frequencies are in the ratios 2, 3, 4, and 5, while the 

 amplitudes are equal. All the bobs are started together 

 from their outside position. For fig. 1, in which all four 

 pendulums are swung, the equations to the trace become 



x = a cos [2pt 4- 7r] 4- a cos [Apt 4- tt] , 

 y=a cos [?>pt 4- 7r] + « cos [5pt 4- ir~\ . 



In figs. 2, 3, 4, and 5 the pendulums A, B, C, and D 

 respectively are at rest, so that the corresponding pairs of 

 equations are derived from those of fig. 1 by deleting the 

 appropriate term. In all five cases the record extends from 

 t = Q to t = 7rjj). The length of the record in time is the same 

 in all the figures up to and including fig. 16. 



