574 Prof. T. R. Lyle on Mechanical Analogy to the 



and as K^^D^d, K.V^D" 1 ^ 



i V i = cos ©,£ — — cos wd 



&>1 © 2 



K 2 V 2 =-~ j {s — b)-± cos corf — (s— a) -^ cos co 2 t k 

 But when £ = 0, Vx = E and Y 2 = 0, therefore 



?i + Qi = _K ; E 



©1 © 2 



which give us 



©j © 2 



©1 C © 2 C 



where a } b, c, and s refer to the triangle. 



Hence for the initial conditions Vi = E, V 2 = 0, Ci = C 2 = 

 when £ = 0, the complete solution is given by 



Vi= — -J (s — a) cos coit + (s—b) cos w 2 t > 



\ 2 =p 2 a— < COS CD J — COS (D 2 t > 



Ef . H L) 



Ci= — K 2 — -J ©^s— a) sin co^ + co^s^-b) sin © 2 £ V 



C 2 =p 2 aK 2 — < —©1 sin © 1 i + © 2 sin © 2 £ >, 



where 



K t M 6 M 



^ = K 2 L 2 " = 5KlM= aL 1 



(see equation III. § 3). 



The complete solution for the pendulum system for 

 analogous initial conditions is obviously given by the same 

 equations. Thus, if when t = 0, t = E, 2 = O, #i = 0, 2 = O, 



J? c ~\ 



#! = — < (s— a) cos corf + (s — b) cos co 2 t > 



' Ef ) 



u 2 =p 2 a— \ cos ©j£ — cos co 2 t >, 



