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The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. The regular motion of pendulums was used for timekeeping and was the world's most accurate timekeeping technology until the 1930s. [ 2 ]
For a point mass on a weightless string of length L swinging with an infinitesimally small amplitude, without resistance, the length of the string of a seconds pendulum is equal to L = g/ π 2 where g is the acceleration due to gravity, with units of length per second squared, and L is the length of the string in the same units.
where L is the length of the pendulum and g is the local acceleration of gravity. All pendulum clocks have a means of adjusting the rate. This is usually an adjustment nut (c) under the pendulum bob which moves the bob up or down on its rod. Moving the bob up reduces the length of the pendulum, reducing the pendulum's period so the clock gains ...
The pendulum, due to its isochronism, could be a much better timekeeper. His son Vincenzio began building a clock, but both he and Galileo died before it was completed. The first pendulum clock was built in 1657 by Christiaan Huygens using a different design. The pendulum clock remained the world's most accurate timekeeper for 300 years, until ...
In 1673 Dutch scientist Christiaan Huygens in his mathematical analysis of pendulums, Horologium Oscillatorium, showed that a real pendulum had the same period as a simple pendulum with a length equal to the distance between the pivot point and a point called the center of oscillation, which is located under the pendulum's center of gravity and ...
The period of the pendulum's swing depends on its length, so a pendulum clock's rate varied with changes in ambient temperature, causing inaccurate timekeeping. The gridiron pendulum consists of alternating parallel rods of two metals with different thermal expansion coefficients, such as steel and brass. The rods are connected by a frame in ...
In most pendulum clocks the rate is adjusted by moving the bob up or down on the pendulum rod. Moving it up shortens the pendulum, making it beat more quickly, and causing the clock to gain time. In the most common arrangement, the bob is attached to the pendulum with an adjustment nut at the bottom, on the threaded end of the pendulum rod.
An important concept is the equivalent length, , the length of a simple pendulums that has the same angular frequency as the compound pendulum: =:= = Consider the following cases: The simple pendulum is the special case where all the mass is located at the bob swinging at a distance ℓ {\displaystyle \ell } from the pivot.