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The real period is, of course, the time it takes the pendulum to go through one full cycle. Paul Appell pointed out a physical interpretation of the imaginary period: [ 16 ] if θ 0 is the maximum angle of one pendulum and 180° − θ 0 is the maximum angle of another, then the real period of each is the magnitude of the imaginary period of ...
In 1673 Huygens had shown that the period of a rigid bar pendulum (called a compound pendulum) was equal to the period of a simple pendulum with a length equal to the distance between the pivot point and a point called the center of oscillation, located under the center of gravity, that depends on the mass distribution along the pendulum. But ...
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 ...
The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on its weight distribution (the moment of inertia about its own center of mass) and the amplitude (width) of the pendulum's swing.
Using as initial conditions () = and ˙ =, the solution is given by = (), where is the largest angle attained by the pendulum (that is, is the amplitude of the pendulum). The period, the time for one complete oscillation, is given by the expression = =, which is a good approximation of the actual period when is small.
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such ...
The same point is called the center of oscillation for the object suspended from the pivot as a pendulum, meaning that a simple pendulum with all its mass concentrated at that point will have the same period of oscillation as the compound pendulum.
The pendulum swings with a period that varies with the square root of its effective length. For small swings the period T, the time for one complete cycle (two swings), is = 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.