;colony/science
;colony/science  / Everyday Physics  / Pendulums
Motion & Forces · Question 19 of 20

Pendulums

A swinging weight ignores how hard you push it and how much it weighs. It answers to one thing only: the length of its string.

Plate V — The pendulum law T = 2π√(L/g) · mass cancels
Drag the bob, change the string, try the Moon — only two things matter.
drag the bob · then let go
FIG. V — THE PENDULUM LAW
String length 1.2 m
Gravity Earth · 9.8 m/s²
Period (one full swing)
2.20s
Swings per minute
27.3/min
Try to cheat: swing it high, swing it low — the time per swing barely changes. Make the string longer and it slows right down. The pendulum only listens to its string and its planet.
The short answer

A swing takes about the same time for every swing, big or small. Make the string longer and it swings more slowly.

What's actually happening

Legend says Galileo, bored in Pisa's cathedral, timed a swinging chandelier against his own pulse and noticed something odd: big swings and small swings took the same time. As the swing dies down, it travels a shorter path — but also moves more slowly, and the two effects cancel almost perfectly. The time per swing, the period, stays fixed.

Stranger still, the weight on the end doesn't matter either. Double the mass and gravity pulls twice as hard on an object that takes twice the force to accelerate — a perfect wash, the same cancellation that makes heavy and light objects fall together. After all the cancelling, only two things survive in the formula: the length of the string and the strength of gravity. T = 2π√(L/g). A one-metre pendulum swings over and back in almost exactly two seconds, anywhere on Earth. Want a slower tick? There is no trick — you need a longer string (period doubles only when length quadruples).

A repeating event that ignores wear, temperature tantrums, and how hard it was pushed is a clock waiting to happen, and for nearly three centuries — from Huygens in 1656 to the quartz era — pendulums were the heartbeat of every serious timepiece. The pendulum had one more revelation to offer: in 1851 Foucault hung a 67-metre one in Paris and let it swing all day. Its swing plane slowly rotated — except it wasn't the pendulum turning. It was the floor. The Earth, rotating underneath, demonstrated for the first time to a public audience that the planet spins.

Try it at home Beat the formula
  1. 1Tie a heavy nut or a few washers to a metre of string and hang it from a door frame. Time ten full swings, divide by ten.
  2. 2Now swap the weight for something twice as heavy: the period refuses to change. Swing it wide, swing it gently: same again.
  3. 3Finally, fold the string to a quarter of its length. The period halves — exactly as √L promised. You've confirmed every term that matters.