(7) The Pendulum
100. The Simple Pendulum.—Any body suspended so as to swing freely to and fro is a pendulum, as in Fig. 81. A simple pendulum is defined as a single particle of matter suspended by a cord without weight. It is of course impossible to construct such a pendulum. A small metal ball suspended by a thread is approximately a simple pendulum. When allowed to swing its vibrations are made in equal times. This feature of the motion of a pendulum was first noticed by Galileo while watching the slow oscillations of a bronze chandelier suspended in the Cathedral in Pisa.
Fig. 81—A simple pendulum.
101. Definition of Terms. The center of suspension is the point about which the pendulum swings. A single vibration is one swing across the arc. A complete or double vibration is the swing across the arc and back again. The time required for a double vibration is called the period. The length of a simple pendulum is approximately the distance from the point of support to the center of the bob.
A seconds pendulum is one making a single vibration per second. Its length at sea-level, at New York is 99.31 cm. or 39.1 in., at the equator 39.01 in., at the poles 39.22 in.
A compound pendulum is one having an appreciable portion of its mass elsewhere than in the small compact body or sphere called a bob. The ordinary clock pendulum or a meter stick suspended by one end are examples of compound pendulums.
The amplitude of a vibration is one-half the arc through which it swings, for example, the arc DC or the angle DAC in Fig. 81.
102. Laws of the Pendulum.—The following laws may be stated: