Experiment 2

A simple pendulum consists of a weight suspended from a string. This experiment shares many similarities with the one described earlier. The pendulum's weight falls, but unlike a freely falling stone, its movement is constrained by the string. The string also forces the weight to rise back up to its original height, from where it will fall again. This sequence repeats multiple times.

While a stone’s fall lasts only briefly, a pendulum can oscillate for a very long time. This makes it relatively straightforward to measure the acceleration due to gravity.

For small angles of deflection, the period of a pendulum's oscillation (the time required for one complete swing) is described by the following formula:

T = 2 * 3.14159 * ((L / g) ** (1 / 2))

Where:
T is the period of the pendulum (seconds),
L is the length of the pendulum (meters),
g is the acceleration due to gravity (m/s²).

Let's calculate the period of oscillation for a 1-meter-long pendulum (39.37 inches) in two cities.

In Anchorage:

2 * 3.14159 * ((1 / 9.825) ** (1 / 2)) = 2.00453305401 seconds

The pendulum completes one oscillation in 2.00453305401 seconds.

In Los Angeles:

2 * 3.14159 * ((1 / 9.796) ** (1 / 2)) = 2.007497963 seconds

The pendulum takes 2.00749796311 seconds per oscillation.

In Los Angeles, the pendulum swings slightly slower than in Anchorage, by about 0.002964909 seconds. While this difference seems negligible at first, after approximately 11 minutes, the pendulums in Anchorage and Los Angeles would start moving out of sync!

Starting the experiments in both cities:

After 11 minutes:

In reality, the desynchronization between the pendulums' oscillations would become noticeable even sooner.

The easiest way to conduct this experiment is to record videos of the same pendulum oscillating in different cities and then compare them. Why is this method so simple? Because you don’t need high precision when constructing the pendulum.

A more accurate approach would be to create two identical pendulums in Los Angeles. Let me explain: Identical pendulums are those that oscillate without any deviation over extended periods. Then, ship one pendulum to Anchorage and compare their oscillations online.

Wikipedia
Pendulum
Kater's pendulum

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