Variably Coupled Vibrations 

 (37) and (38) are satisfied by 



TT . 7T 



€'• 



j. *=£, (39) 



From (27) and (39) in (37) we obtain 



whence 



G- _ (b -/»» + 3) -2ao t P ~) 

 H~~ 2aotp-(b-m 2 -8J [ 



E _(b-m 2 + 8)-2accp f 

 F ~~ 2aa/3 — (&-m a — 8) J 



(40) 



AT , E G 



Note F = g. 



(iv.) Lower bob displaced ; upper bob free. 



We may here write 



a?p djf dz 



y=f, z=- 1 -.,, dt =Q, j^O&r^O. 



Then, proceeding as before, we obtain 



2 ^ 



, " P ./=E sine + F sin <£ j 



/= G sin e + H sin <f> j 

 = Ep cos e + F# cos ^ | 

 = Gcp cos e + H<? cos <f> I 



Equations (41) and (42) are satisfied b} r 



«=|, *-j, .._..■ («> 



From (27) and (43) in (41) we obtain 



(42) 



