Pendulum Simulator
Explore pendulum motion with an interactive simple pendulum simulator. Adjust length and gravity, view the period formula, and learn how pendulums work.
Pendulum period formula
T = 2π√(L / g)
The ideal simple pendulum formula estimates the period T, or the time for one complete swing. L is the pendulum length in meters and g is gravitational acceleration in m/s². For small angles, this formula is accurate enough to calculate pendulum period in many classroom examples.
What is a simple pendulum?
A simple pendulum is a mass suspended from a fixed point by a light string or rod. Pull it to one side and gravity pulls it back toward the lowest point, creating a repeating swing.
At small angles, a simple pendulum simulator can show motion that is close to simple harmonic motion. The restoring force grows as the pendulum moves away from the center, then pulls it back through equilibrium.
What affects pendulum motion?
The main values that affect ideal pendulum motion are length, gravity, and starting angle. Length changes how far the bob travels along its arc. Gravity changes how strongly it is pulled back toward the center.
Friction and air resistance matter in real life, but the basic pendulum formula usually starts with an ideal model so the relationship is easier to see.
Length vs period
Length has the clearest effect on period. A longer pendulum swings more slowly, while a shorter pendulum swings more quickly. Because the formula uses a square root, making the pendulum four times longer doubles the period.
For example, a 1 m pendulum on Earth has a period of about 2.01 seconds. A 0.25 m pendulum has a period of about 1.00 second.
Does mass affect pendulum period?
In the ideal simple pendulum model, mass does not significantly affect the period. A heavy bob and a light bob with the same length should swing with the same period if friction and air resistance are ignored.
That result can feel surprising, which is why changing values in a pendulum period calculator is helpful. Length and gravity change the timing; mass is not part of the small-angle period formula.
How to use this simulator
Adjust the pendulum length and gravity, then watch how the animation and period readout respond. Use small starting angles when you want the motion to match the standard pendulum formula closely.
Try changing one value at a time. That makes it easier to see whether the period changed because of length, gravity, or a larger starting angle.
Practical examples
Calculate pendulum period on Earth
For L = 1 m and g = 9.81 m/s², T = 2π√(1 / 9.81), which is about 2.01 seconds.
Short classroom pendulum
For L = 0.25 m on Earth, the period is about 1.00 second. Shortening the length makes the pendulum swing faster.
Same pendulum, weaker gravity
For L = 1 m and Moon gravity near 1.62 m/s², the period is about 4.94 seconds.
FAQ
Is this a simple harmonic motion simulator?
For small starting angles, the pendulum is a good approximation of simple harmonic motion. At larger angles, the motion still repeats, but the simple formula becomes less exact.
How do I calculate pendulum period?
Use T = 2π√(L / g), where L is length and g is gravity. Enter those values in the simulator to compare the formula with the live motion.
Why does mass not appear in the pendulum formula?
In the ideal model, the gravitational force and inertia both scale with mass, so mass cancels out. That is why length and gravity control the period instead.