Experimental Mechanics / A Course of Lectures Delivered at the Royal College of Science for Ireland

by Robert S. Ball

589. If a weight be attached to a piece of string, the other end of which hangs from a fixed point, we have what is called a simple pendulum. The pendulum is of the utmost importance in science, as well as for its practical applications as a time-keeper. In this lecture and the next we shall treat of its general properties; and the last will be devoted to the practical applications. We shall commence with the simple pendulum, as already defined, and prove, by experiment, the remarkable property which was discovered by Galileo. The simple pendulum is often called the circular pendulum.

THE CIRCULAR PENDULUM.

Fig. 82.

590. We first experiment with a pendulum on a large scale. Our lecture theatre is 32 feet high, and there is a wire suspended from the ceiling 27' long; to the end of this a ball of cast iron weighing 25 lbs. is attached. This wire when at rest hangs vertically in the direction o c ([Fig. 82]).

I draw the ball from its position of rest to a; when released, it slowly returns to c, its original position; it then moves on the other side to b, and back again to my hand at a. The ball—or to speak more precisely, the centre of the ball—moves in a circle, the centre being the point o in the ceiling from which the wire is suspended.

591. What causes the motion of the pendulum when the weight is released? It is the force of gravity; for by moving the ball to a I raise it a little, and therefore, when I release it gravity compels it to return to c it being the only manner in which the mode of suspension will allow it to fall. But when it has reached its original position at c, why does it continue its motion?—for gravity must be acting against the ball during the journey from c to b. The first law of motion explains this. ([Art. 485]). In travelling from a to c the ball has acquired a certain velocity, hence it has a tendency to go on, and only by the time it has arrived at b will gravity have arrested the velocity, and begin to make it descend.

592. You see, the ball continues moving to and fro—oscillating, as it is called—for a long time. The fact is that it would oscillate for ever, were it not for the resistance of the air, and for some loss of energy at the point of suspension.

593. By the time of an oscillation is meant the time of going from a to b, but not back again. The time of our long pendulum is nearly three seconds.

594. With reference to the time of oscillation Galileo made a great discovery. He found that whether the pendulum were swinging through the arc a b, or whether it had been brought to the point a´, and was thus describing the arc a´ b´, the time of oscillation remained nearly the same. The arc through which the pendulum oscillates is called its amplitude, so that we may enunciate this truth by saying that the time of oscillation is nearly independent of the amplitude. The means by which Galileo proved this would hardly be adopted in modern days. He allowed a pendulum to perform a certain number of vibrations, say 100, through the arc a b, and he counted his pulse during the time; he then counted the number of pulsations while the pendulum vibrated 100 times in the arc a´ b´, and he found the number of pulsations in the two cases to be equal. Assuming, what is probably true, that Galileo’s pulse remained uniform throughout the experiment, this result showed that the pendulum took the same time to perform 100 vibrations, whether it swung through the arc a b, or through the arc a´ b´. This discovery it was which first suggested the employment of the pendulum as a means of keeping time.