People are often surprised to learn that the time it takes a pendulum to swing back and forth—called the pendulum’s period—doesn’t depend on the mass of the pendulum bob or on how far the pendulum swings.
You can prove this to yourself by swinging a bottle of water on a string: First try it with a full bottle, then dump out half of the water. Then try little swings and big, wide swings. Does the pendulum’s period change?
The equation for the period (T) of a simple pendulum is:
where T is the period in seconds per swing, L is the length (in meters) and g is the acceleration due to gravity (9.8 m/s2).
The frequency F of a pendulum is the number of times it swings all the way back and forth in one second (expressed in swings per second). Frequency is the inverse of period, or 1/T. So the equation for calculating the frequency of a pendulum is the inverse of the formula above, or
Squaring both sides,
Solving for L,
You can use this equation to calculate the length of a pendulum for a given frequency. For example, the longest pendulum of your Pendulum Snake swings back and forth 24 times in 30 seconds. Frequency is expressed in swings per second, so 24 swings/30 seconds = 0.8 swings/second. Using 9.8 m/s2 for g and 0.8 swings/second for F in the equation gives you a length of 0.387 meters, or 38.7 centimeters.