178 Forced Vibrations Experimentally Illustrated. 



Inserting the values of p 2 , n 2 . and kn given in (9), 

 equation (13) becomes 



V. Experimental Results. 



The photographs shown in figs. 7-12, PL IX., were taken 

 with the apparatus arranged as in fig. 2 so as to keep the 

 value of / due to the big bob the same for each responding 

 pendulum. One kind of light bob only was used, viz. the 

 sharp-angled paper cones. The curves obtained on the plates 

 differed so little from those used in the first arrangement 

 that it seemed unnecessary to repeat experiments with bobs 

 having different dampings. Fig. 8 represents the resonance 

 curve in duplicate to the right and left of the central line, and 

 was obtained by a time exposure. The maximum swing of 

 the lower cones is seen to be greater than that of the upper 

 cones. This is because the vertical abscissse are lengths as x 

 in (10) and not the squares of the frequencies asp 2 in (8). 

 These curves agree with equation (10). 



Figs. 7, 9, 10, 11, 12, show instantaneous views taken 

 by flash-powder. Fig. 7 shows the state when the heavy bob 

 was passing the centre towards the right. The figure shows 

 the bob slightly beyond the centre, but this is a small fraction 

 of the amplitude and involves a still smaller fraction of the 

 quarter period. Then it is well seen from the curve (a) that 

 the upper responding bobs are in phase with the driving bob 

 and therefore at the middle of their swing towards the right, 

 (b) that the lower ones are also at the middle of their swing 

 though they are in opposite phase and moving to the left, 

 and (c) the middle bobs are at the end of their swing with a 

 lag of about 90° phase angle behind the driver. 



Fig. 9 shows the curve obtained with the large bob at the 

 end of its swing to the right. It will be noticed that the 

 upper bobs are less displaced from the centre than the lower 

 ones. This asymmetry was to be expected from the form of 

 equation (14), with which it is in entire accord. 



Figs. 10-12 are intermediate stages with the large bob 

 partly displaced. They show the gradual melting of the 

 curve from the case of exaggerated resonance with the bobs 

 all on one side, fig. 7, to the state of fig. 9 with half the 

 bobs on each side. The set of figures 7, 10, 11, 12, 9 corre- 

 spond to intervals of about the tenth of a second in the 

 motions of the actual pendulums. 



Nottingham, 

 May 28, 1918. 



