334: Mr. L. 0. Jackson on 



(ii.) Loiver bob struck. 

 We may here write 



, = 0, , = 0, § = „, §=0for*=0. 



Then, proceeding as before, we find 



= Esin6 + Fsin^)> 



= Gc sin e + H sin </> I 



= Er> cos e + F^ cos </> ; 



j . . . . . (do) 

 v=Gj> cos e + H<? cos </> j 



Equations (32) and (33) are satisfied by 



6=0, <^ = 0. ..... (34) 



From (27) and (34) in (33) we obtain 



= Ep + F?, 



v = Gp + B.q, 



w 



hence 



E= "P ■ . , , 



X ^' +?) ! (35) 



q(.-p 2 + q*) ' j 



Thus we see that the ratios of the amplitudes of the quick 

 and slow motions for the y and z vibrations respectively are 

 given by 



G_ -g(-p 2 + b ) _ _ (b + m 2 + 8Xb + m 2 -8 )n 

 H~~ p(-q* + b) " (b + m 2 -8)(b + m 2 + 8)i \ 



E _ -q _ r b + m 2 -8 l* [" ' ^ 36 ' 



F " p '" U + m 2 + sJ J 



(iii.) Upper bob displaced; loicer bob free. 

 We may here write 



y =«/, ../, |=0, J=0fo ri = 0. 



Then, proceeding as before, we find 



/'— E sin e + F sin 6 ) 



' ■ r • o.TT • I " • * • ' (37) 



a/ = (jt sm e + Jl sin <p ) 



= Kp cos e + F^ cos cf> i 



[■.... (3o) 

 = Gjo cos e + H^ cos </> 



