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XXV. Acoustical Notes. — VI. 

 By Lord R-ayleigh, F.R.S.* 



Forced Vibrations. 



IF free vibrations be represented by cos nt, and if the 

 forced vibration dne to a force acting in a very long, 

 period be cos pt, c then the actual forced vibration will be 



n 2 cos pt 

 n 2 —p 2 



It is here implied : — 



(1) That in all cases the forced vibration takes its period! 

 from the force, whatever may be the natural period. 



(2) That if the forced vibration be the slower, viz. if p<n r 

 the phase is the same as if the vibration were infinitely slo\v r 

 in which case the vibrator would be situated at any instant 

 of time in the position where the momentary force would 

 permanently maintain it. 



(3) That if the forced vibration be the quicker (p>n) y 

 the phase of the actual vibration is the opposite of that defined 

 in (2). 



(4) That if the force have nearly the period of the free 

 vibrations, the effect is much enhanced. Indeed, according 

 to the formula it would become infinite, which means that 

 forces of a viscous character, never really absent, must now 

 be brought into the reckoning. 



So far as I am aware, illustrations of this important theory f 

 have usually been wanting in lecture demonstrations, except 

 as regards (4). I have found that if we employ as vibrator a 

 magnet with attached mirror, as used for example in Thomson 

 galvanometers, the whole may readily be brought before a 

 large audience. 



With the aid of an external magnet, whose distance could; 

 be varied, the frequency of (complete) vibration was adjusted 

 to 10 per minute, the vibrations being manifested by the 

 motion of a spot of light reflected from the mirror on to a 

 scale in the usual manner. The force brought to bear upon 

 the vibrator had its origin in the revolution of a rather long 

 permanent magnet, situated at some little distance, and so 

 mounted as to be capable of rotation. Xo particular situation 

 is necessary, but the action of the magnet is simplest in certain 

 special cases, as when its centre is at the level of the sus- 

 pended magnet and in the direction of the screen. The plane- 



* Communicated by the Author. 



f Young's Lectures on Natural Philosophy, p. 578 (1807). 



