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I. § 19.] PENDULUM- VIBRATION 39 |
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we may without any perceptible error suppose the end of the pendulum to move in a horizontal straight line instead of in a circular arc, i.e. along d'A instead of dA. To take an actual case, let us suppose the pendulum to be 10 ft. long, and its extent of swing 1 inch on either side of its vertical position. An easy geometrical calculation shows that the end of the pendulum will never be as much as
-— th of an inch out of the horizontal straight line
drawn through it in its lowest position. This is a vanishing quantity compared to the length of the pendulum; we may, therefore, safely regard the vibration as performed along d'A instead of dA. Such a vibration, though executed in a straight line instead of in the arc of a circle, may be properly called a pendulum-vibration, as expressing the law according to which it takes place. This law admits of simple geometrical illustration as follows. Let a ball, or other small object, be attached to some part of a wheel revolving uniformly about a fixed horizontal axis, so that the ball goes round and round in the same vertical circle with constant velocity. If the sun is in the zenith, i. e. in such a position that the shadows of all objects are thrown vertically, the shadow of the ball on any horizontal plane below it will move exactly as does the bob of a pendulum. |
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