224 PROFESSOR FORBES ON A SEISMOMETER FOR MEASURING 



Therefore 



(ds\ 2 

 Tt) = ~ 



When s = and y = 0, -r- V (for the point A begins to move with a velo- 

 city V), 



d~e ~ ~^ 



ds 1 . 1 s 



dt= .,. . ; and e= 7- sm =-, A/ + c'. 



When s = 0, t = .-. d = 0, 



V 



s = 77/r n (/#*) (5). 



V 

 The greatest value of s = ~T~T> ............ (&*) 



occurs when J $ .t= 90, 270, &c. 



orwhen '=-'' &c ......... (6> 



In order that the movement should not be oscillatory, V . t must be always 



-^ 90 for all values of t ; or V ^ ^ 

 When is infinite ^ ^ 0, which is impossible, if be a redressing force at all. 



III. To determine the motion of the pendulum after the motion of the base 

 suddenly stops. 



Whilst x varies uniformly (with velocity = V) 



" 



Let x abruptly cease to increase when t = T (and then let s = S) 



T) ...... (7). 



By (1) the displacement S is then ( y _VT) ....... (8), 



y =. V T + S = V T - sin (V <f> . T). 

 v <p 



The absolute velocity of C is then ^ = V - ^L cos (V . T) V tf> 



. . . (9); 



