Variably Coupled Vibrations. 



295 



on the position of the point of suspension of the gravity 

 pendulum*. 



The paper includes 32 photographic traces of the motion 

 of the gravity pendulum under various conditions of coupling 

 and starting. 



II. Theory. 



Equations of Motion and Coupling, 



For the gravity and elastic pendulums, let the masses of 

 the bobs be M and N, let the length of the simple pendulum 

 equivalent to PM be r, and at time t let the linear displace- 

 ments of M and N be y and z respectively ; further, let the 



Fig. 1. 



linear displacement of P be olz. It should be noted that 

 the displacement of the bob N oE the elastic pendulum has 

 always the positive sense as shown in fig. 1. 



Then for small oscillations, and considering PN as straight, 

 the equations of motion may be written 



"2* 



*(*==) -o,. 



S5J+.HA = 1^»=5). 



* The bob of this gravity pendulum carried an electric lamp and 

 a lens, and left on a plate below it a photographic record of its motion. 



