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For comparison of the approximation to the full solution, consider the period of a pendulum of length 1 m on Earth (g = 9.806 65 m/s 2) at an initial angle of 10 degrees is (). The linear approximation gives
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]
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.
In the linear approximation, the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude. This property, called isochronism, is the reason pendulums are so useful for timekeeping. [7] Successive swings of the pendulum, even if changing in amplitude, take the same amount of time.
A pendulum wave is an elementary physics demonstration and kinetic art comprising a number of uncoupled simple pendulums with monotonically increasing lengths. As the pendulums oscillate, they appear to produce travelling and standing waves , beating , and random motion.
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 ...
The parameter stands for in an ideal pendulum, and in a compound pendulum, where is the length of the pendulum, is the total mass of the system, is the distance from the pivot point (the point the pendulum is suspended from) to the pendulum's centre-of-mass, and is the moment of inertia of the system with respect to an axis that goes through ...