What Is the Formula for Finding the Time It Takes for One Pendulum Swing?


Quick Answer

The time that it takes a simple gravity pendulum to complete one left and right swing, or oscillation, can be determined for small angles of deflection by the formula T = (2 x pi) times the square root of L/g. T represents the time for one complete oscillation, L is the length of the pendulum and g is the local strength of gravity. The formula can be rearranged to read as T2 = 4pi2/g x L.

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Full Answer

When the bob of a pendulum is pulled away from its resting place, or equilibrium position, and then released, gravity acts on it as a restoring force. The mass of the bob combined with the force of gravity causes it to swing back and forth across its original resting point. In the case of small swings, the oscillation time is the same for successive swings of different lengths. The period of time for each swing is not dependent on the amplitude of the swing. This characteristic is referred to as isochronism, and accounts for the usefulness of pendulums in time-keeping devices.

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