264 Prof. Barton and Miss Browning on Coupled 



Though both the types of pendulum are broadly alike and 

 fall equally under the equations (95) and (96), their individual 

 details, as dependent on the values of A, B, and C, are some- 

 what different as already shown in the separate examinations. 

 It is specially noticeable that in the double-cord pendulum, 

 with equal pendulum lengths and masses, everything is inter- 

 changeable and, of the two superposed vibrations when 

 coupled, one has the unaltered period of the pendulums if 

 separated. In the cord and lath pendulum there is no such 

 interchangeability, and both the vibrations superposed when 

 coupled differ in period from those which would occur if the 

 pendulums were separated. This is more like the electrical 

 case. 



VII. Forced Vibrations : Special Case of Coupled 

 Vibrations. 



It is interesting to note how the case of coupled vibrations 

 reduces to that of forced vibrations when the coupling is 

 small and the driving mass is much greater than the driven 

 mass whose vibrations are forced. Thus in equations (95) 

 and (96) let B be small but so as to be appreciable with 

 respect to the very small mass P but inappreciable with 

 respect to the much larger mass Q. 



Then (96) reduces to 



Qgp+C*=0, (98) 



giving as a solution 



2 = Ksinn£, say (99) 



Then, this used in the right side of (95) gives 



P^+Ay = BKsinn*, . . . . (100) 



which is one form of the equation of motion for forced 

 vibrations. 



By hanging a simple pendulum with bob of very small 

 mass near A of the double-cord pendulum, we could imitate 

 the experiment in which Dr. Fleming's Cymometer detects by 

 resonance the two superposed vibrations in a pair of closely- 

 coupled inductive circuits. The pendulum imitating the 

 cymometer would show maximum responses for two lengths 

 corresponding to the quick and slow vibrations. 



For cases where P is much less than Q and B small but 

 not quite negligible in comparison with either, the equations 

 (27)-(29) for the double-cord pendulum and (55)-(57) for 



