Simulation · as seen in our pendulum-wave reel
Pendulum wave
15 pendulums, one release. Each one makes one more swing per minute than the one above it. When do they line up again?
Time0:00.0
Lines up in60.0 s
Line-ups0
The top one always makes 51 swings a minute, each next one makes one more.
What you're seeing
You're looking down on pendulums that hang from one straight rail (top view). Each row is one pendulum, and they are all let go together from 10°. With the default 15, the longest one (top, red) is 34.3 cm and makes 51 full swings a minute. Each one below is a little shorter and makes one swing more, down to 65 swings for the shortest (21.1 cm, violet). The numbers on the left count full swings.
- Their swing counts drift apart by one per minute, so they make snakes. At 30 s they form two lines: the ones that have made a whole number of swings are back on the start side, the half-numbers are on the far side. At exactly 60 s all of them are back where they started.
- The lengths come from the exact period of a 10° swing, T = 4·√(L/g)·K(sin 5°), not the textbook 2π·√(L/g). The textbook lengths are about 0.4% too long, and at 60 s those pendulums are still about a tenth of a swing behind. Tick the box to see it.
- Each pendulum solves θ″ = −(g/L)·sin θ with RK4 at a fixed step of 1/4800 s (g = 9.81 m/s², no friction). 60 s is exactly 288,000 steps, and the page never steps past a line-up. That's why it lands on 60.0 s, not 59.98.