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Concept
Kater's pendulum
Summary
A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 for use as a gravimeter instrument to measure the local acceleration of gravity. Its advantage is that, unlike previous pendulum gravimeters, the pendulum's centre of gravity and center of oscillation do not have to be determined, allowing a greater accuracy. For about a century, until the 1930s, Kater's pendulum and its various refinements remained the standard method for measuring the strength of the Earth's gravity during geodetic surveys. It is now used only for demonstrating pendulum principles.
A pendulum can be used to measure the acceleration of gravity g because for narrow swings its period of swing T depends only on g and its length L:
So by measuring the length L and period T of a pendulum, g can be calculated.
The Kater's pendulum consists of a rigid metal bar with two pivot points, one near each end of the bar. It can be suspended from either pivot and swung. It also has either an adjustable weight that can be moved up and down the bar, or one adjustable pivot, to adjust the periods of swing. In use, it is swung from one pivot, and the period timed, and then turned upside down and swung from the other pivot, and the period timed. The movable weight (or pivot) is adjusted until the two periods are equal. At this point the period T is equal to the period of an 'ideal' simple pendulum of length equal to the distance between the pivots. From the period and the measured distance L between the pivots, the acceleration of gravity can be calculated with great precision from the equation (1) above.
The acceleration due to gravity by Kater's pendulum is given by,
where T1 and T2 are the time periods of oscillations when it is suspended from K1 and K2 respectively and l1 and l2 are the distances of knife edges K1 and K2 from the center of gravity respectively.
Official source
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