Table of Contents
Pendulum Period
The period of a simple pendulum is the time required for one complete back-and-forth oscillation. For small amplitudes, the period depends only on the length of the pendulum and the local gravitational acceleration. This remarkable property, discovered by Galileo, made pendulums the most accurate timekeeping devices for nearly 300 years.
A 1-meter pendulum has a period of approximately 2 seconds (1 second each way), which is why grandfather clocks use pendulums of about this length. The period is independent of the mass of the bob and, for small amplitudes, independent of the swing amplitude. This property is called isochronism.
Formulas
Period on Different Bodies
| Location | g (m/s²) | Period (1m pendulum) |
|---|---|---|
| Earth | 9.81 | 2.006 s |
| Moon | 1.62 | 4.935 s |
| Mars | 3.72 | 3.261 s |
| Jupiter | 24.79 | 1.264 s |
Frequently Asked Questions
How accurate is the small-angle formula?
For amplitudes under 15°, the error is less than 0.5%. At 30°, the error is about 1.7%. At 45°, about 4%. At 90°, the error is about 18%. For precision applications, use the series expansion or exact elliptic integral formula.
How was the meter originally defined?
There was a proposal (never adopted) to define the meter as the length of a pendulum with a half-period of exactly one second. This gives L = g/π² ≈ 0.994 m, remarkably close to the actual meter. The pendulum's elegant relationship between length and time made this an attractive, though ultimately impractical, definition.