38 Professors Perry and Ayrton on a neglected Principle 



the earthquake vibrations at tlio beginning, they do after some 

 time if the earthquake only lasts long enough, and continues 

 to be exactly the same pure harmonic motion. 



Section B. 

 Let the friction be such that 



then the solution of the differential equation becomes 

 En 2 cos (n l t+ tan" 1 -f^C) 



Making 

 and 



when 

 we find 



and 



dx 



dx U? 



£ = 0, 



G_^+3ny 



E~~ (^ + w 2 ) 25 



E 7iJ + ?z 2 . 



Let the springs be strong, and 



n=10ni, 



then 



^,-oME^ + _n^-_Ecos^-tan-yJ. 



If the springs are weak, and 



n 1 = 10n, 

 then 



_?l* /10300 , 100 \ E / _ , .20\ 

 A, = e 10 E (l020l + lOT^V" IOI COS (^ + tan 99> 

 These results are of the same nature as before : with the 

 strong springs we see, since g- 10? M j s small compared with 

 ■J-g4, that x represents the displacement due to the earthquake 

 only; with the weak springs, when t is small, the natural vi- 

 brations of M preponderate and mask the earthquake-effect ; 

 but as t increases, these vibrations become smaller relatively 

 to those due to the earthquake, so that the weak springs will 

 eventually record the earthquake if it only lasts long enough. 



