I. Pendulum Experiment Instructions (Quantitative measurement version)

Videos (Windows Media Player Format, may not work on Apple machines)

Materials

Setup

The Pendulum experiments were used by Galileo to demonstrate the law of inertia and the equal rate of fall of heavy and light objects. Galileo also discovered the mathematical relationships between the period, the amplitude , and the length of the string.

I. Varying Amplitude (how far it swings) .

A. Let a pendulum swing for a while and watch it as it wears down. Does it nearly return to the point where it was let go after the first swing? What principle of Galileo’s does this illustrate? Why would Aristotle have disagreed?

As it starts to swing less and less does the period (the time for it return to its starting point) of its oscillation decrease?

Legend has it that he first discovered that the period is independent of the amplitude while watching this lamp in a cathedral in Pisa.

B. Varying the Amplitude and Measuring Period: Video Instructions

1. Medium Amplitude. Have a timer measure a 15 second period. Drop the pendulum from medium height when the timer says start and count the number of complete swings it makes before they say stop.

2. Low Amplitude: Make the same measurement, this time dropping the pendulum from less height.

3. High Amplitude: Make the same measurement, this time dropping the pendulum from more height. Don’t start it so high it doesn’t swing freely.

Does the period vary with amplitude? Can you figure out why? Why do you think this is important?

II. Varying the length of the string: Video Instructions

Make long pendulum, and measure how many swings it makes in 15 seconds. Decrease the length of the string by ½ and measure again. Decrease by another ½ and measure again. You should be able to decrease it by ½ one more time.

Does the number of swings change the by the same amount each time you cut the string length in half. Can you figure out the mathematical relationship between the two? Is it surprising that there should be a regular relationship between the two that doesn’t vary?

III. Different Weights: Video Instructions
 
"...repeat many times the fall through a small height in such a
way that I might accumulate all those intervals of time that elapse
between the arrival of the heavy and light bodies respectively at
their common terminus, so that this sum makes an interval of time
which is not only observable, but easily observable." Galileo

"...two balls, one of lead and one of cork, the former more than
a hundred times heavier than the latter, and suspended them by
means of two equal fine threads, each four or five cubits long.
 
"This free vibration repeated a hundred times showed clearly that
the heavy body maintained so nearly the period of the light body
that neither in a hundred swings nor even in a thousand will the
former anticipate the latter by as much as a single moment, so
perfectly do they keep step." Galileo

1. Control. First release two identical pendulums at the same time. How many swings do they stay in sync? How far out of sync do they get after 15 seconds? Why do you think they get out of sync a little? Why is it important to do two identical ones first?
2. Different weights. Release the heavy nut with the lighter ring clamp. How many swings do they stay in sync? How far out of sync do they get after 15 seconds? What does this show? Why was this result important to Galileo?
3. If you want, try some of the lighter pendulums. What do you think causes the difference in results?

IV. Free Fall

Try dropping some objects of different weights at arms length and see which hit the ground first. You will have some plastic balls, some metal balls, and the metal pendulums. You can also use any other materials you have at hand. Do they all hit the ground at the same time? Can you explain why there are differences? Why did Galileo think the pendulum experiment so much more convincing than this one?

Here is a set of simulations of the Leaning tower of Pisa Experiments from the Nova Site.

Additional Resources:

Here is the Rice University site on Galileo’s Pendulum Experiments