Does Length Affect the Period of a Pendulum?
The length of the pendulum is directly correlated to its period as per the pendulum equation: T = 2π√(L/g), where T is the period of the pendulum, L is its length, and g is the gravitational constant 9.8 m/s2. Regardless of the weight of the pendulum bob, otherwise known as the weight at the end of the string, the deciding factor of the period of the swing is length, as it is the only variable in the stated equation.
A simple pendulum is modeled by physicists as a point mass suspended from a rod or string, which has negligible mass. If the rod or string has a significant mass, then it must be modeled differently. This system is considered a resonant system with a specific resonant frequency, which means that depending on the length of the string or rod, the pendulum will swing within a specific range of oscillation values, as commonly observed in clocks.
In 1581, Galileo discovered that the period and frequency of a pendulum is unaffected by the amplitude while watching a chandelier swing during a church service. He noticed that the chandelier would swing faster when it was swinging widely and slower when it moved less distance. He timed the period of the oscillation during both instances with his heartbeat and found the number of beats per period was roughly the same when swinging widely and moving less distance.