Simple pendulum lab
Pull the bob aside and let go, time the swings with a stopwatch, and find how the period depends on length, angle and gravity.
This interactive 3D pendulum lab needs a browser with WebGL. The explanation of the model and the questions below do not.
How a simple pendulum works
A simple pendulum is a small heavy bob on a light string that swings under gravity. For small angles its period is T = 2π√(L/g): it grows with the square root of the length, falls with the square root of gravity and does not depend on the mass. For larger angles the period gets longer, and the exact value needs an elliptic integral.
In this virtual lab you do what a student does at a real bench: time several swings with a stopwatch that has a 0.01 s least count, read the length on a ruler, record the numbers, plot T against L with error bars and estimate g. Switch to the Moon or Mars and see the swing slow down.
Frequently asked questions
How does the period of a pendulum depend on its length?
The period grows with the square root of the length: T = 2π√(L/g) for small angles. Quadrupling the length doubles the period, and a graph of T² against L is a straight line with slope 4π²/g.
Does the mass of the bob change the period?
Not without drag: the mass cancels out of the equation of motion. With air drag a lighter bob of the same material loses amplitude faster, because drag acts on a smaller mass.
Why does a large release angle make the period longer?
The restoring force is proportional to sin θ, which is smaller than θ. The bob is pulled back less than the small-angle formula assumes, so each swing takes longer: about 7 % longer at 60°.
How can a pendulum measure the acceleration of gravity?
Time many swings for several lengths, plot T² against L and fit a straight line. Then g = 4π² divided by the slope. Timing 10 or 20 swings instead of one cuts the relative error of the stopwatch reading.
How accurate is this simulation?
It solves the full nonlinear equation with a symplectic integrator. The period agrees with the exact elliptic-integral value within 0.1 %, and without drag the energy changes by less than 0.1 % over a simulated hour. Both limits are checked by automated tests.