Pendulum Clock

Timing one swing badly is the classic way to get a wrong answer.

1. Hang a dense bob on fine line from a firm support.
2. Measure the length from the pivot to the CENTRE of the bob.
3. Time 20 complete swings and divide by 20.

The most surprising result in the whole exercise.

1. Keep the length identical.
2. Swap the bob for one two or three times heavier.
3. Re-time twenty swings.

Now vary the one thing that does matter, and plot it.

1. Time the pendulum at several lengths — 10, 20, 40, 80 cm.
2. Note that doubling the length does NOT double the period.
3. Plot period against the square root of length; it should be a straight line.

T = 2π√(L/g)

Rearrange the formula and your pendulum becomes a gravimeter.

1. Take your best length and period measurements.
2. g = 4π²L / T²
3. Compare with 9.81 m/s².

The isochronism everyone quotes is an approximation. Find where it fails.

1. Time twenty swings at a small amplitude, a few degrees.
2. Repeat at a large amplitude, 40 degrees or more.
3. Compare carefully.

Galileo observed around 1602 that a pendulum's swing time barely depends on its amplitude, and near the end of his life sketched a pendulum clock; his son Vincenzio attempted a model after his death. Christiaan Huygens designed a working clock in 1656, had it built by Salomon Coster, and patented it in 1657. He published the full theory in Horologium Oscillatorium in 1673, including the cycloidal correction and the theory of the centre of oscillation.

The improvement was enormous. Clocks went from losing roughly fifteen minutes a day to losing about fifteen seconds, and the anchor escapement — which allows a much smaller swing — brought that down further. That is why clock faces gained a minute hand: before pendulums, minutes were not worth displaying.

What it could not do is keep time at sea. A pendulum depends on gravity and a steady support; a rolling deck ruins both. Huygens tried marine pendulum clocks repeatedly and they failed, and the longitude problem waited for John Harrison's spring-driven chronometers a century later — a different solution to the same problem, covered in its own blueprint.

What replaced it: the quartz oscillator, and then the caesium atomic standard. But the logic is unchanged — find something with a stable natural period, count its cycles. A quartz watch is a pendulum clock whose pendulum is a vibrating crystal.