The Great Pendulum Experiment

Pendulums are easy to make and fun to learn about. A pendulum consists of a
weight on the end of a string. What could be simpler? The longer the string,
the longer the time between swings. Believe it or not, the amount of weight,
within reason of course, has nothing to do with the time per swing.

So what makes a pendulum work? The answer is gravity.

There are only two important things to measure for a pendulum. The first is its
length, and the second is its period, or the time it takes for one complete swing.

We have to be careful to define what we mean by a complete swing. Here is an easy
way to think of this. Assume that the pendulum is at the leftmost top of its swing.
One complete swing will take it from where it is to its rightmost top and then
back to its leftmost top again. The time it takes to make this trip out and back
is called the period. In other words, the period is the time it takes the pendulum
to make one complete swing

The Challenge
Here is your challenge. Using only a stopwatch and a pendulum, determine the
length of a pendulum that will produce a period of exactly one second.

Since we will be measuring times that are too short, even for a stopwatch, we will
use the strategy of measuring the time for ten periods and then, by dividing by
ten, find the time for one. "Why ten?", because it is convenient and very easy.
To divide by ten we need only move the decimal point one place to the left. For
example, if it takes 17 seconds for ten complete swings, the period, or time for
one complete swing is 1.7 seconds. Neat?

The second strategy we will employ will be graphic interpolation. Interpolation
is a big word which simply means that we will graph time per swing versus pendulum
length by plotting data points that are near, but above and below the desired value
of one second. Once these points have been plotted we will draw a smooth line
through them and from this line determine the exact length that relates to a
period of one second.

Let's get started.
First we must perform a few experiments. We will collect data for the periods of
pendulums ranging from 5 to 25 inches. Next we will plot pendulum length versus
period.

After plotting your points, draw a smooth line through them. Move horizontally
across the one second line until you reach your curve. When you do, drop down
to the horizontal axis to find the pendulum length in inches of a one second pendulum.