🕰️ Simple Pendulum Calculator

Calculate period, frequency, and angular frequency of a simple pendulum

Physics Calculator

🕰️ Simple Pendulum Calculator

Formula

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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