Pendulum Clock
Pendulums kept time in clocks for 300 years. Change the length of the string, how far you pull it back and which planet you are on, then count the swings with the stopwatch.
- Swings
- 0
- Stopwatch
- 0.00 s
- Measured T
- Count a swing
- Formula T
- 2.000 s
The maths, live
Period T = 2π√(L ÷ g)T = 2π√(0.994 ÷ 9.81) = 2.000 sStopwatch T = 2 × time ÷ swingsLet it swing and count!Big swings are a bit slowerat 10°: T = 2.004 s (+0.2%)A 0.994 m pendulum on Earth takes 1 second for each swing, so a full there-and-back takes 2 s. That is why grandfather clocks are so tall!
How it works
Gravity pulls the bob back towards the middle, it overshoots, and gravity pulls it back again. The time for one full there-and-back swing is the period, T = 2π√(L ÷ g). Only the length and gravity matter: a heavier bob swings at the same rate.
A pendulum 0.994 m long takes 1 second for each swing on Earth, so its period is 2 s. Clockmakers call it a seconds pendulum. The simple formula works best for small swings: pulled back a long way, a pendulum takes a little longer.
Try this
- Make the string four times longer. What happens to the period?
- Take the seconds pendulum to the Moon. Would a grandfather clock run fast or slow there?
- Compare a 10° swing with a 90° swing. How much slower is the big one?