The Pendulum — Time a Swing and Weigh Gravity

Around 1602 the young Galileo watched a lamp swinging in Pisa cathedral and timed it against his pulse. Whether it swung wide or narrow, each swing took the same time. That discovery — isochronism — is what makes a pendulum a clock, and you are about to measure it yourself.

Tie a small heavy weight (a steel nut, a ball bearing, or a fishing weight) to the end of a piece of string, and hang it from a fixed point like a doorframe or a clamp so it can swing freely. Measure the length of the string from the pivot to the middle of the weight with a tape measure and write it down — call it L.

Pull the weight to one side by a small angle (about 10-15 degrees — small swings work best) and let go. With a stopwatch, time how long TWENTY complete back-and-forth swings take, then divide by 20 to get the time of one swing (the period). Timing 20 and dividing makes your result far more accurate than timing just one. Do it two or three times and average. Then change the string length and measure again.

A few things your experiment reveals. (1) The bob's MASS does not matter — a heavy and a light bob of the same length keep identical time, because gravity pulls harder on the heavy one but also has more mass to move, and the two effects cancel. (2) The period grows with the square ROOT of the length: to make a pendulum swing twice as slowly you must make it four times as long — which is why a tall grandfather clock ticks once per second with a bob about a metre down. (3) Isochronism (equal times) only holds for SMALL swings; past about 20 degrees the period slowly lengthens, which is why pendulum clocks keep their swing narrow. (4) Because a pendulum's tick depends on gravity, the very same swing measures how strong gravity is, runs the pendulum clock that timed the world for 300 years, reveals the Earth's rotation in Foucault's giant pendulum, and detects earthquakes in a seismometer.