# Definition:Circular Error of Pendulum

Jump to navigation
Jump to search

## 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 $6$