Pendulum Physics Simulator

How It Works: The Science of Pendulums

A pendulum is one of the most elegant demonstrations of physics in action. Whether it's a grandfather clock or a child on a swing, the same simple rules of nature govern every back-and-forth motion. This simulator lets you explore exactly how length, gravity, and initial angle shape a pendulum's behaviour.

The Period Formula

The time it takes a pendulum to complete one full swing (out and back) is called its period, denoted T. For small angles the motion is beautifully predictable:

Where L is the length of the string in metres and g is the local gravitational acceleration in m/s². Notice what's missing: the mass of the bob and the starting angle (for small swings) don't matter at all. Galileo was the first to discover this remarkable property — two pendulums of the same length will always keep the same time, no matter how heavy their bobs are.

Gravity Across the Solar System

Gravitational acceleration varies enormously from world to world. On the Moon (g ≈ 1.62 m/s²) the same 2-metre pendulum swings nearly 2.5× more slowly than on Earth (g = 9.81 m/s²), while on Jupiter (g ≈ 24.8 m/s²) it swings more than 1.6× faster. Use the celestial presets in the simulator to compare periods side by side, and try the "Calculate L" tool to reverse-engineer the exact string length needed to hit a target period on any world.

Real-World Applications

For centuries the pendulum was the most accurate timekeeper humanity had. Christiaan Huygens invented the pendulum clock in 1656, reducing daily timekeeping error from minutes to seconds. Scientists also use pendulums to measure local gravity with high precision — geologists still swing specially crafted gravimeters to map underground density changes, helping locate oil reservoirs and underground caverns.