Calculate period, frequency, and angular frequency of a simple pendulum
Physics Calculator
Simple pendulum — Quick answer
A simple pendulum is a mass on a string, swinging under gravity. The period depends only on length and gravity, not the mass.
T = 2π × √(L / g) f = 1/T = 1/(2π) × √(g/L)
T — period (seconds) for one full swing
L — pendulum length (metres)
g — gravitational acceleration (9.81 m/s² on Earth)
f — frequency (Hz)
Worked example: 1 m long pendulum on Earth: T = 2π × √(1/9.81) = 2π × 0.319 = 2.006 s. Frequency = 1/2.006 = 0.498 Hz. A grandfather clock with a 2 s tick uses a ~1 m pendulum.
This calculator uses the standard simple pendulum calculator formula:
Pendulum Period Formula
T = 2π × √(L / g)
Frequently Asked Questions
What is the formula for a simple pendulum's period?⌄
T = 2π√(L/g), where L is the pendulum length in metres and g is gravitational acceleration (9.81 m/s² on Earth). The period does not depend on mass or amplitude for small swings.
How long must a pendulum be to have a period of 1 second?⌄
Rearranging: L = g × (T/2π)² = 9.81 × (1/2π)² ≈ 0.248 m (about 24.8 cm).
Does the mass of a pendulum affect its period?⌄
No. For a simple pendulum, period depends only on length and gravitational acceleration, not the mass of the bob.
What is the period of a 1-metre pendulum on Earth?⌄
T = 2π√(1/9.81) ≈ 2.006 seconds. A 1-metre pendulum completes approximately one full swing every 2 seconds.
How does gravity affect pendulum period?⌄
Lower gravity means a longer period (slower swing). For example, on the Moon (g=1.62 m/s²), a 1-metre pendulum has T = 2π√(1/1.62) ≈ 4.94 seconds.
What is the difference between period and frequency?⌄
Period (T) is the time for one complete oscillation. Frequency (f) is the number of oscillations per second. f = 1/T. For example, T=2s gives f=0.5 Hz.
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