THE 

 LONDON, EDINBURQH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



APRIL 1883. 



XXXIII. On Maintained Vibrations. By Lord Rayleigh, 

 F.R.S., Professor of Experimental Physics in the University 

 of Cambridge* . 



WHEN a vibrating system is subject to dissipative forces, 

 the vibrations cannot be permanent, since they are 

 dependent upon an initial store of energy which suffers gra 

 dual exhaustion. In the usual equation 



d 2 6 , d9 { 2a n ',' 



d?+*4i+*W (l) 



k is positive, and the solution indicates the progressive decay 

 of the vibrations in accordance with the exponential law. In 

 order that the vibrations may be maintained, the vibrating 

 body must be in connexion with a source of energy. This 

 condition being satisfied, two principal classes of maintained 

 vibrations may be distinguished. In the first class the mag- 

 nitude of the force acting upon the body in virtue of its 

 connexion with the source of energy is proportional to the 

 amplitude, and its phase depends in an approximately con- 

 stant manner upon the phase of the vibration itself ; in the 

 second class the body is subject to influences whose phase is 

 independently determined. 



The first class is by far the more extensive, and includes 



* Communicated by the Author. 

 Phil. Mag. S. 5. Yol. 15. No. 94. April 1883. S 



