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156 BEATS OF SIMPLE [VII. § 76. |
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in fact, to compound two sets of pendulum-vibrations whose periods are not exactly equal. Let us fix on a moment of time at which the two component vibrations are in complete accordance, and suppose that a resultant vibration is just commencing from left to right. It will be convenient to call this an outward, and its opposite an inward swing. Since the periods of the two component vibrations are unequal, one of them will at once begin to gain on the other, and therefore, directly after the start, they will cease to be in complete accordance. It is easy to ascertain what their subsequent bearing towards each other will be, by considering two ordinary pendulums of unequal periods, both beginning an outward swing at the same instant. Let A be the slower, B the quicker pendulum. When A has just finished its outward swing, B will have already turned back and performed a portion of its next inward swing. Thus, during each successive swing of A, B will gain a certain distance upon it. When B has, in this manner, gained one whole swing, i.e. half a complete oscillation, upon A, it will begin an inward swing at the moment when A is commencing an outward swing. The two vibrations are here, for the moment, in complete opposition. After another interval of equal length, B, having gained another whole swing, will be one complete oscillation ahead of A, and they will |
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