﻿506 



Dr. J. H. Vincent and Mr. 0. \V. Jude on 



of the beating- pendulums is equal to the frequency of the 

 motion at right angles. In the second, the mean frequency 

 is twice that of the third frequency, while in the third class 

 the mean frequency is half that of the remaining frequency. 

 The fourth class will contain examples involving four 

 frequencies such that simple relations hold between the 

 means of the frequencies of oppositely-placed pendulums. 



Index of Diagrams 36 to 46. 



No. 



Frequencies 



of beating 



pendulums 



as 



Mean freq. 



of beating 



pendulums. 



Other 



frequency. 



Pendulums 

 recording. 



Initial Conditions. 



36 



37 

 38 

 39 

 40 

 41 

 42 

 43 



;.! 



- 



P + h 



r and 



1 7 



1 2p + h 

 V and 



\ and 



1 

 j p 



P 



2p+2h 



2p+h 



2 



P 

 p+k 



2p+k 



All recording except B in No. 37. 



•\ D releases C. "" 

 J B releases A. 



N | 

 i 



1 



1 All starting 

 r together. 



C releases J). 



1 A releases B. 

 J ) 



Displacements 



all negative 



■ except 



pendulum C 



in No. 42. 



The other Frequency their Mean. 



In fig. 36 pendulums B and D are tuned in unison, while 

 A and C have frequencies respectively greater and smaller 

 by equal amounts. B and D release A and C as they pass 

 through their mean positions. All four amplitudes are 

 initially equal. In this case we have allowed the pen to be 

 in contact with the prepared surface from the commence- 

 ment of the motion of the pendulums B and D. The tracing- 

 needle begins by drawing a circle of radius 2a and is removed 

 when it has traced the approximate straight line along y. 

 If friction had been completely eliminated the length of this 

 line would have been 4a. Counting time from the simul- 

 taneous release of A and C, the equations to the trace are 



#=acos [{p + h}t + 7r~] +acos \_\p— Aj£ + 7r], 



y=a cos [p(t 4- ir/2p) + tt] + a cos \_p(t 4- tt/2/?) 4- 7r] , 



the record extending to t = ir/2Ji. The displacement along x 



