CHAPTER VI. 



VIBRATIONS. 



VIBRATIONS are alternate movements backward and forward. 

 If with the finger we depress one scale-pan of a balance, it will 

 continue to move alternately up and down over the same path 

 for a long time after the finger is removed, or if we pull the scale- 

 pan to one side and then release it, it will swing backward and 

 forward for a time; or suppose a ball, hung by a fine wire, be 

 twirled by the finger so as to'twist the wire; let go of it, and, 

 speedily untwisting the wire, it will go on for a time twisting it 

 up the other way; these alternate motions are vibrations. 



The pendulum is a body hanging from a fixed point upon 

 which it can swing freely. The fixed point is called the point of 

 suspension, and the point in the pendulum which vibrates as if 

 only under the influence of its own gravitation and inertia, is 

 called the center of oscillation, and the length of the pendulum 

 is the distance between the point of suspension and the center of 

 oscillation. The center of oscillation is generally a little below 

 the center of gravity of the pendulum ball. 



The pendulum vibrates under the in- 

 fluence of gravitation and inertia. Sup- 

 pose a ball at M (see Fig. 2) to repre- 

 sent a pendulum hung from the fixed 

 point, C, by a cord MC. Now, if this 

 ball be lifted to the point A and for a 

 moment held there, the force of gravity 

 will act upon it in a vertical direction. 

 FIG. 2 \^ We will represent this force by the line 



AB, and resolve it into two compo- 

 nents, shown by the lines AD and AE. The force, AD, acts length- 

 wise of the string without effect to move the ball ; the other force, 

 (50) 



