1. The period of a pendulum is not affected by its mass or the material of which the pendulum is made.
2. For small amplitudes, the period is not affected by the length of the arc through which it swings.
3. The period is directly proportional to the square root of the length. Expressed mathematically, t/t´ = √l/√l´.
103. Uses of the Pendulum.—The chief use of the pendulum is to regulate motion in clocks. The wheels are kept in motion by a spring or a weight and the regulation is effected by an escapement (Fig. 82). At each vibration of the pendulum one tooth of the wheel D slips past the prong at one end of the escapement C, at the same time giving a slight push to the escapement. This push transmitted to the pendulum keeps it in motion. In this way, the motion of the wheel work and the hands is controlled. Another use of the pendulum is in finding the acceleration of gravity, by using the formula, t = π√(l/g), in which t is the time in seconds of a single vibration and l the length of the pendulum. If, for example, the length of the seconds pendulum is 99.31 cm., then 1 = π√(99.31/g); squaring both sides of the equation, we have 12 = π2(99.31/g), or g = π2 × 99.31/12 = 980.1 cm. per sec., per sec. From this it follows that, since the force of gravity depends upon the distance from the center of the earth, the pendulum may be used to determine the elevation of a place above sea level and also the shape of the earth.
Important Topics
1. Simple pendulum.
2. Definitions of terms used.
3. Laws of the pendulum.
4. Uses of the pendulum.