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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]
The distance between these two conjugate points was equal to the length of a simple pendulum with the same period. As part of a committee appointed by the Royal Society in 1816 to reform British measures, Kater had been contracted by the House of Commons to determine accurately the length of the seconds pendulum in London. [6]
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.
The period of a mass attached to a pendulum of length l with gravitational acceleration is given by = This shows that the period of oscillation is independent of the amplitude and mass of the pendulum but not of the acceleration due to gravity, g {\displaystyle g} , therefore a pendulum of the same length on the Moon would swing more slowly due ...
When calculating the period of a simple pendulum, the small-angle approximation for sine is used to allow the resulting differential equation to be solved easily by comparison with the differential equation describing simple harmonic motion.
If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the string is constrained to be tangent to one of its arches, and the pendulum's length L is equal to that of half the arc length of the cycloid (i.e., twice the diameter of the generating circle, L = 4r), the bob of the pendulum also traces a cycloid path.
Schematic of a cycloidal pendulum. The tautochrone problem was studied by Huygens more closely when it was realized that a pendulum, which follows a circular path, was not isochronous and thus his pendulum clock would keep different time depending on how far the pendulum swung. After determining the correct path, Christiaan Huygens attempted to ...
Drawing of pendulum experiment to determine the length of the seconds pendulum at Paris, conducted in 1792 by Jean-Charles de Borda and Jean-Dominique Cassini. From their original paper. They used a pendulum that consisted of a 1 + 1 ⁄ 2-inch (3.8 cm) platinum ball suspended by a 12-foot (3.97 m) iron wire (F,Q).