Laws of the Pendulum
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
P-91
2025-11-05
43
Demonstration. - Suspend side by side four pendulums made by fastening lead balls to the ends of strong threads (Fig. 1). Make two of them 1 m. long, one 50 cm., and one 25 cm. Measure the distance from the point of suspension to the middle of each ball. Vibrate pendulums A and B. Do two pendulums of the same length vibrate in the same time? Vibrate A and B so that one swings about twice as far as the other. Do they still vibrate in the same time? Vibrate B (or A) and C. Does a pendulum half as long as another vibrate in half the time? Vibrate B (or A) and D. What is the relation between the time of vibration of one pendulum and that of another one fourth its length?
From an extension of the above experiment, it is found that the relation between the time of vibration, or period, of a pendulum and its length may be expressed by the formula
in which t is the time, in seconds, of one complete vibration, and I is the length of the pendulum. In a pendulum of this type the length is from the point of support to the middle of the ball.
Another pendulum of length I' will vibrate in the same place in the time
and hence we get the proportion
The times of vibration of two pendulums are proportional to the square roots of their respective lengths, and are independent of their weights and of their amplitudes of vibration.
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