PENDULAR VIBRATIONS. 



545 



gradually then faster, until it crossed the vertical again, at 

 the end of a second and commenced a similar excursion on 

 its other side, at the end of which it would be back at 1, 

 and in just the same position, and ready to repeat exactly 

 the swing, with which we commenced. A pendulum 

 thus executes similar movements in equal 

 periods of time, or its vibrations are 

 periodic. A full swing on each side of 

 the position of rest constitutes a complete 

 vibration, so the vibrational period of a 

 second's pendulum is two seconds: at the 

 end of that time it is precisely where it 

 was two seconds before, and moving in 

 the same direction and at the same rate. 

 It is clear that by examining such a curve 

 we could tell exactly how the pendulum 

 moved, and also in what period if we knew 

 the rate at which the paper on which its 

 point wrote was moving. The vertical 

 line 0-1-2 is called the abscissa; per- 

 pendiculars drawn from it and meeting 

 the curve are ordinates: equal lengths on 

 the abscissa represent equal times; where 

 an ordinate from a given point of the 

 abscissa meets the curve, there the writing 

 point was at that moment; where succes- 

 sive ordinates increase or decrease rapidly 

 the pendulum moved fast from or towards 

 its position of rest, and vice versa. Simi- 

 larly, any other periodic movement may be 

 perfectly represented by curves; and since 

 the form of the curve tells us all about the 

 movement, it is common to speak of the "form of a vibra- 

 tion," meaning the form of the curve which indicates its 

 characters. Periodic vibrations (Fig. 150), whose ordi- 

 nates at first grow fast, then more slowly, next dimin- 

 ish slowly and then faster, and represented by a symme- 

 trical curve on one side the abscissa, which is repeated 



FIG. 150. 



