How to play Pendulum Clock
- Choose a test and read the length, the period, or g on the card.
- A pendulum swinging through a small angle has a period T = 2π·√(L ÷ g): only the length and g matter.
- Type your prediction and press Start. A period run lasts one full swing; a length run lasts the period the pendulum should have.
- Watch the graph and the ghost: if your answer is right, the pendulum is back where it started exactly when the run ends.
What sets a pendulum's beat?
Pull a pendulum aside and gravity pulls it back towards the bottom, harder the further it is pulled: for small angles the pull is proportional to the distance, which is exactly the condition for simple harmonic motion. The bob then swings back and forth with a steady rhythm, θ = θ₀·cos(2π·t ÷ T), and the period is T = 2π·√(L ÷ g). Three surprises hide in that formula. The width of the swing doesn't matter, as long as it stays small, which is why Galileo could use a pendulum to keep time. The mass doesn't matter either: a heavier bob is pulled harder, but it is just as much harder to speed up. And the period goes with the square root of the length, so to double it you need four times the length. Because g is in the formula, a pendulum also measures gravity: on the Moon, where g is a sixth of Earth's, the same pendulum swings about 2.5 times more slowly.
A focused learning model
The string is light and doesn't stretch, the bob is small, and there is no air resistance or friction. The bob is let go 10° from the bottom, small enough for T = 2π·√(L ÷ g) to hold. When a period is asked, the run lasts one full swing of the pendulum; when a length is asked, your pendulum swings for the period it should have, so a right answer ends exactly where it began. Lengths are to scale up to 1.55 m. Answers within 2% are right. g = 9.8 m/s² on Earth and 1.62 m/s² on the Moon. Plays in real time.