170 Prof. Barton and Miss Browning on 



& 



syntonic jars, Hertz's oscillator and resonator, wireless- 

 telegraphy. Possibly we might be justified in adding to 

 this list the sensitive parts of the ear and eye. 



It accordingly seems desirable to have some quite simple 

 vivid mechanical illustration that exhibits qualitatively and 

 quantitatively the chief phenomena concerned. Types of 

 such experiments are here described. 



The apparatus consists of a single heavy driving pendulum 

 and a number of light driven ones, of graduated lengths all 

 suspended from the same tightly stretched cord. Thus the 

 various effects of tuning and mistuning may be observed 

 simultaneously. By a steady view the variation of amplitude 

 with tuning is seen in spite of the phase differences involved. 

 By a stroboscopic view (or illumination) the variation of 

 phase with tuning is exhibited to a small class (or a larger 

 audience). 



The above remarks refer to the experiment in various 

 forms. For confirmation of exact quantitative relations the 

 experiment needs arranging with special attention to certain 

 details. It is then found to confirm the theory in every 

 respect. , 



By changing to responding bobs of greater density the 

 increased sharpness of resonance with smaller damping is 

 shown. 



Photographic reproductions are given showing four time 

 exposures and eight instantaneous views of the responding 

 pendulums. These exhibit all the features enumerated above. 



II. General Theory. 



The equation of a single particle of mass m with restoring 

 force s times its displacement y and r times its velocity 

 under the action of a sustained harmonic impressed force, 

 may be written 



m J +r !l + ^= Fsin ^ • • • • (1 > 



Sr + »J^-/«n-, .... (2) 



where r s , . F , q . 



2k =— , p z =—, and /= — . . . . (o) 

 in r m • m 



The solution of this may be written 



y= v/u^+(^n +E "" si "^ +e) ' • • (4) 



or, 

 {Displacement} = ( Foroed Vibration) + (Free Vibration).. 



