244 



Professor Edwin H. Barton 



[March 8, 



do this pass along the first row in Table I. taking the cases of the 

 pendulums there shown. 



If a pendulum bob is pulled aside and let go, it returns towards 

 its zero position under the combined effect of gravity and its slant 

 suspension. On reaching the zero position with a certain velocity 

 it overshoots the mark because the bob has inertia. Thus a free 

 vibration is set up. This may continue until slowly extinguished by 

 friction which is operating all the time to diminish the swings. 

 Next let the point of suspension of a pendulum be moved shghtly 

 to-and-fro by periodic forces. Then the pendulum would be set in 



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Table I. 



vibration and kept going. Further, the motions would settle down 

 to a quite definite amplitude and phase. These are the forced yihm- 

 tions. Their amplitude would depend upon that of the point of 

 suspension and also on the tuning. By tuning is meant the degree 

 of agreement ])etween the period natural to the pendulum and that 

 of the forces applied to it. The closer the tuning between them the 

 better the response. Upon the tuning depends also the phase of the 

 forced vibrations. When the forces alternate appreciably slower than 

 the vibrations natural to the pendulum the two are almost in like 



