Definition:Circular Error of Pendulum
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Definition
The period of a pendulum $P$ is dependent upon the angle from the vertical from which the bob is released.
That period of $P$ is described by Motion of Pendulum as being:
- $T = 2 \sqrt {\dfrac a g} \, \map K {\map \sin {\dfrac \alpha 2} }$
where:
- $a$ is the length of the rod of $P$
- $\map K k$ is the complete elliptic integral of the first kind.
The circular error of $P$ is the difference between $T$ and its approximate period as described by period Approximate Motion of Pendulum:
- $T' = 2 \pi \sqrt {\dfrac a g}$
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.21$: The Cycloid: Footnote $6$