[ 246 ] 



XXVIII. Vibrations under Variable Couplings Quantitatively 

 Elucidated by Simple Experiments. By Edwin H. Barton, 

 JJ.Sc, F.B.S., Professor of Physics, and H. Mary 

 Browning, B.Sc, Heymann Scholar, University College, 

 Nottingham *. 



[Plates XV.-VL] 



Contents. 



Page 



I. Introduction 246 



II. Equations for Electrical Circuits 247 



III. Previous Mechanical Analogies 250 



IV. Theory of Double-Cord Pendulums 252 



Description. 



Equations of Motion and Coupling. 

 Solution and Frequencies. 

 Initial Conditions. 



V. Theory of Cord and Lath Pendulums 257 



Description. 



Equations of Motion and Coupling. 

 Solution and Frequencies. 

 Initial Conditions. 



VI. Comparison of the Pendulums 263 



VII. Forced Vibrations : Special Case of Coupled 



Vibrations 264 



VIII. Experimental Methods and Kesults 265 



Double-Corel Pendulum. 

 Cord and Lath Pendulum. 

 IX. Summary 269 



I. Introduction. 



LET us consider a vibrational system of two degrees of 

 freedom, mechanical or electrical, formed by the 

 coupling of two separate systems. Further, let the restor- 

 ing forces be proportional to the displacements and let all 

 resistances be negligible. Then it is well known that the 

 simultaneous differential equations of motion of the coupled 

 system lead to a solution expressing the superposition of two 

 simple harmonic motions one or both of whose frequencies 

 differ from those characteristic of the separate systems. 



But, obvious as this may be to the trained mathematician, 

 it is extremely difficult to bring it home to the average 

 electrical student. Yet to such the matter is of extreme 

 importance at the present time in connexion with wireless 

 telegraphy. Hence any simple mechanical systems that can 



* Communicated by the Authors. 



