Pendulum Period Formula
Calculate the period of a simple pendulum with T = 2pi sqrt(L/g).
Learn how length and gravity affect swing time with examples.
The Formula
The period of a simple pendulum depends only on the length of the string and the acceleration due to gravity. It does not depend on the mass of the bob or the amplitude of the swing (for small angles).
Variables
| Symbol | Meaning |
|---|---|
| T | Period — time for one complete swing (measured in seconds, s) |
| π | Pi (approximately 3.14159) |
| L | Length of the pendulum (measured in meters, m) |
| g | Acceleration due to gravity (9.81 m/s² on Earth) |
Example 1
A grandfather clock has a pendulum 1 meter long. What is its period?
Identify: L = 1 m, g = 9.81 m/s²
T = 2π × √(1 / 9.81)
T = 2π × √(0.1019)
T = 2π × 0.3193
T ≈ 2.006 s (about 2 seconds — this is why grandfather clocks use 1 m pendulums)
Example 2
A playground swing has chains 3 meters long. How long does one full swing take?
Identify: L = 3 m, g = 9.81 m/s²
T = 2π × √(3 / 9.81)
T = 2π × √(0.3058)
T = 2π × 0.5530
T ≈ 3.47 s
When to Use It
Use the pendulum period formula for oscillation and timing problems:
- Designing clocks and timing devices
- Calculating the period of swings, chandeliers, or hanging objects
- Measuring gravitational acceleration by timing a pendulum
- Understanding simple harmonic motion in physics courses