Vibrations elucidated by Simple Experiments. 263 



These values put in (66) and (67) give the special solution 



y (l + « + ^)(p 2 -? 2 ) ' I 



(l + « + a 2 )-(l + a )m 2 | 



+ M , ■ 2W 2 2\~ a C0S 9^ 



(l + a + a 2 )(p 2 -^ 2 ) * J 



( p 2-m 2 ){(l + «)m 2 -(l + a+a 2 )g 2 } 

 * = m 2 «(l + « + a 8 )(p 2 - ? 2 ) aC ° S ^ 



(m 2 -? 2 ){(l + * + a> 2 -(l + «)m 2 j- | 



(92) 



(93) 

 (94) 



So the ratios of the amplitudes of the quick and slow 

 vibrations in the y and z motions are given respectively by 



E _ (l + aV-(l + tt + * , )y* 



F~(l + a + a 2 )p 2 -(l + a)m 2 ' " ' 

 and 



H" (m 2 — 5 2 ) ^ ( 1 + « + « 2 )p 2 — (1 + «)?72 2 }■ 

 Note the contrast of (93) and (94) with {88). 



VI. Comparison of the Two Types of Coupled- 

 Pendulums. 



Referring to equations (27) and (28), and (55) and (56), 

 we see that the two types of model under examination have 

 equations of motion of the form 



pg+Ay = B*, (95) 



Q'g+Cr-By (96) 



And in each case we have for the coupling 7 the relation 



B 2 

 ? 2 =AC < 97 > 



These may be compared with equations (l)-(3) for the 

 electrical case. It is there seen that the coupling involves 

 the inductances L and N but is independent of the 

 capacities. Whereas in (95) and (96) the A and C involve 

 g/l, g/r, and gjs (which are comparable to the reciprocals of 

 the capacities) as well as the masses P and Q (comparable to 

 L and N). 



