Pendulum Period Calculator
Calculate the small-angle period of a simple pendulum.
Formula
T = 2π√(L/g), valid for small oscillation angles.
Understanding Pendulum Period
The period of a simple pendulum is the time required for one complete back-and-forth oscillation. For small angles, the period depends mainly on pendulum length and gravitational acceleration, not on the mass of the bob.
Example Calculation
A pendulum 1 m long has T = 2π√(1/9.80665), giving a period of about 2.006 seconds.
Factors and Interpretation
A longer pendulum swings more slowly, so its period increases with the square root of length. Stronger gravity shortens the period. The small-angle approximation is most accurate when the initial displacement angle is modest; large amplitudes produce a slightly longer true period.
Frequently Asked Questions
Does bob mass affect the period?
Not in the ideal simple-pendulum model.
Why is the formula called a small-angle approximation?
Its derivation assumes sinθ is approximately equal to θ when θ is measured in radians.
What length should I measure?
Measure from the pivot point to the bob’s center of mass.
Related Tools
Formula and Practical Limits
For a simple pendulum at small angles, T = 2π√(L/g). Large swing angles, air resistance and pivot friction cause departures from the small-angle idealization.