Vibrations elucidated by Simple Experiments. 261 



of the coupled system have frequencies which differ from 

 each other and from those of the separate systems even when 

 they are alike. 



Hence, in these broad features this system of the cord and 

 lath pendulum is in agreement with the electrical system of 

 coupled circuits. But in the closer details differences show 

 themselves, as may be noted by comparison of (75) with 



(18). 



Initial Conditions. — Since for this cord and lath pendulum 

 the equations are not symmetrical, the phenomena may 

 depend upon which bob receives a blow or displacement 

 when starting. We accordingly treat each in turn. 



(i.) Upper Bob Struck. — We may here write as follows : — 



y=0 , z=0> ! =0 , g=», for *=0. . . (77) 

 These conditions in (66)- (69) give equations satisfied by 



6=0j ^ =0 ; E= _^L F=V^Y . (78) 



p(p 2 -q 2 ) q(p 2 -q 2 ) 



So, inserting these values in (66) and (67), we have for 

 the special solution 



nvav 



V- — r~2 ¥T S111 P t + r~2 2V~ sm <!*> I 



(p 2 -q 2 )p ^ (f~q 2 )q 

 (p 2 — m 2 )v . , (m 2 — o 2 )v . 



~ = (2 — 2~r~ sm P l + — — sf- sin Qt- J 



[p 2 -q 2 )p r \P'-q 2 )q * 



If the amplitudes of the quick and slow ^-vibrations are Gl- 

 and H, we have 



V~ p and H-(m 2 - 2 >- * • • ( 80 > 

 (ii.) Lower Bob Struck. — Here we may write 



y=0, 2 =0, &=«, g=0, for f=0. . . (81) 



These, inserted in (66) to (69), give equations satisfied by 



6=0] ^ =0) E = -^> F=<£=^. . (82) 



(p 2 -q 2 )p 0> 2 -? 2 )? ■ ' 



