Fig. 86.
621. Holding, as shown in the figure, a in one hand and b in the other, I release them simultaneously, and you see the result,—they both meet at c: even if I bring a up to e, and bring b down close to c, the result is the same. The motion of a is so rapid that it arrives at c just at the same instant as b. When I bring the two balls on the same side of c, and release them simultaneously, a overtakes b just at the moment when it is passing c. Hence, under all circumstances, the times of descent are equal.
622. It will be noticed that the string attached to the ball b, in the position shown in the figure, is almost as free as if it were merely suspended from o, for it is only when the ball is some distance from the lowest point that the side arcs produce any appreciable effect in curving the string. The ball swings from b to c nearly in a circle of which the centre is at o. Hence, in the circular pendulum, the vibrations when small are isochronous, for in that case the cycloid and the circle become indistinguishable.
LECTURE XIX.
THE COMPOUND PENDULUM AND THE
COMPOSITION OF VIBRATIONS.
The Compound Pendulum.—The Centre of Oscillation.—The Centre of Percussion.—The Conical Pendulum.—The Composition of Vibrations.
THE COMPOUND PENDULUM.
Fig. 87.
623. Pendulous motion must now be studied in other forms besides that of the simple pendulum, which consists of a weight and a cord. Any body rotating about an axis may be made to oscillate by gravity. A body thus vibrating is called a compound pendulum. The ideal form, which consists of an indefinitely small weight attached to a perfectly flexible and imponderable string, is an abstraction which can only be approximately imitated in nature. It follows that every pendulum used in our experiments is strictly speaking compound.