38 Prof. Barton and Miss Browning on Coupled 



II. Theory of General Case. 



Equations of Motion and Coupling. — The double-cord 

 pendulum was shown in figs. 1 and 2, p. 253, of the first 

 paper (Phil. Mag., Oct. 1917). The equations of motion 

 and coupling were there given as equations (25), (26), 

 and (29) (pp. 253-254). They may now be rewritten as 

 follows : — 



p§ + ¥=o, (i) 



Q§ + Q<^=o, (2) 



«._ £PQ_ f3 > 



The ratio of the masses of the bobs may be expressed by 

 p = Q/P and the lengths of the suspensions for the y and z 

 vibrations by i)l and I respectively, the droop of each bridle 

 being ftl. 



Then y-fflfi> . , z-0la fJLX 



6= ~W~' * = ~^ (4> 



Further, neglecting masses of suspensions, connector, and. 

 bridles, co must satisfy 



Qg{^f — co) = Fg(o}- 

 or 



pg{^r — co)=g{(o- 



Then (4) in (5) gives 



0). ) 



wl= y+npz (6> 



And (6) in (4) gives 



W+V + VP + Ppv) 9 ■''':"> 

 (/3 + v + V p)z-fy 

 r ~K/3 + y + yp + 8p V ) W 



Inserting frictional term 2k'Pdi//dt in (1), putting g/l = m 2 

 and dividing (1) by P and (2) by Q, then (7) and (8) in (1) 

 and (2) give 



d "y + 2*'^ + * + /> + #> m 2 7/ _ §P m l z /o^ 



d? + dt + i3 + v + V p+/3yp my ~ /3 + y + yp + /3 V p Zs W 



d 2l . ^ + 7y + ^p _ m> y&n 2 ^ 



dt 2 p + y+yp + pyp fi + y + yp + fiyp 



