Free Pendulum Wave | Pendulums In and Out of Step

How it works

Open this page. Fifteen pendulums are already swinging. At first they move as one, then the wave begins.
Slide Time to any moment of the cycle. At half the cycle the balls form two rows, at a third three groups. Drag the picture to look from another side.
Set Pendulums, Cycle, and Swings to build your own wave. Turn on Sound to hear each swing, then save a PNG.

One swing more per cycle

Each pendulum makes one swing more per cycle than the pendulum before it. In the classic setup the longest swings 51 times in 60 seconds, the next 52 times, and the shortest 65 times. After 60 seconds every pendulum has finished a whole number of swings, so they all line up again.

Why the length sets the rhythm

A small swing of a pendulum takes 2π√(L/g) seconds. Only the length and gravity count, not the weight of the ball, and for small swings not how far it swings. A shorter string means a quicker swing. A pendulum that swings a quarter faster needs a string about two thirds as long.

Waves, rows, and groups

The pendulums drift a little further out of step with every swing. Side by side they look like a wave running along the row. Halfway through the cycle every other pendulum is half a swing ahead, so the balls stand in two rows. At a third of the cycle they fall into three groups, at a quarter into four. The info panel names the pattern as it appears.

Frequently asked questions

Why do the pendulums line up again?

In one cycle each pendulum completes a whole number of swings: 51, 52, and so on up to 65. At the end of the cycle every one of them is back where it started, at the same moment.

How long are the strings?

For the classic wave, 51 to 65 swings in 60 seconds, the longest string is about 34 cm and the shortest about 21 cm. Cycle and Swings change the lengths, and the picture scales to fit.

Does a bigger swing change the pattern?

A wide swing takes slightly longer than a small one. The simulation sets each length for the Angle you choose, so the cycle still closes. A real pendulum wave is let go from a small angle for the same reason.

What does Friction do?

It is air resistance. The swings shrink while their timing barely changes, so the pattern fades without falling apart. At zero friction the wave keeps going.

Does this upload anything?

No. The pendulums are drawn on a canvas in your browser. Save downloads a PNG. Edit opens that image in the PictorX editor.