Forced Vibrations Experimentally Illustrated. Ill 



Finally, to avoid unequal treatment of the displacements 

 of the various bobs K, their distances from the camera must 

 be nearly equal. Hence they should be set well away from 

 the camera but as close together as will avoid entanglement. 



As regards the length JK for the best tuning with DE, it 

 should be noticed that no equality will be apparent on the 

 photographs. First, because E is not shown at all, and 

 second, because the length DO which is shown is greatly 

 magnified relatively to the lengths JK. To confirm the 

 theory in this respect actual measurements of these lengths 

 should be made on the apparatus itself. 



Consider the time after the dying away of the free 

 vibrations. Then equation (4) has reduced to 



/"sin (nt — S) 

 ^/{(f-n>y+{2knfY ' ' ' 



which expresses the forced vibration only. 



Case I. Take first the variation of amplitude y, of the 

 forced vibration with frequency natural to the responding 

 system. We have already from (6), k = ri\ /7r, let us now 

 write 



p 2 =g/%, n 3 =g/l, then kn=g\ /irl. . . . (9) 



And (9) in (8) leads to 



7T 2 fl 2 X 2 



y- 



(8) 



yi 



2 



Case II. For the second case take the instant when the 

 heavy bob D is undisplaced but is moving in the positive 

 direction. Then we may write sinn£ = 0, and cosn£=l. 

 Inserting these in (8) we have 



-/sin 8 _ —f(2kn) 



*/2 : 



</{(f-n 2 ) 2 +{2kn) 2 } (p 2 -n 2 ) 2 + (2kny 



Then using (9), (11) becomes 



-27r i f\ lx 2 



f = 



g\>ir 2 (l-xy + 4\ 2 x 2 \ 



(11) 



(12) 



Case III. Consider next the instant when the heavy 

 bob D has its maximum displacement in the positive 

 direction. Then we may write cosn£ = 0, and sinn£ = l. 

 Substituting these in (8) we have 



v _ / cosg - A?-* 2 ) nVi 



y % ~ /f/^2 ™2\2i/OZ,vA2 / ~2 ^2\2 _i_ C9L m \'2' ' \ XO S 



x /{(p^-.n 2 ) 2 + (2kn) 2 (p 2 -n 2 ) 2 + (2kn)*' 

 Phil. Mag. S. 6. Vol. 36. No. 212. Aug. 1918. 



N 



