A simple pendulum is a small mass attached to a string of length l. When hanging straight down, the simple pendulum is in stable equilibrium. When it is displaced  moved to one side  the force of gravity, its weight, and the tension in the string are the only forces that act on it.For small displacements, the net foce is proportional to how far it has been moved from equilibrium. This fits our definition for a simple harmonic oscillator.
Therefore, for small amplitudes, a simple pendulum is another example of a simple harmonic oscillator.
Interestingly, the period of a simple pendulum is independent of the mass m. Only the length l and the acceleration of gravity determine the period.
As for all simple harmonic oscillators, the period is independent of the amplitude.






(C) 2003, Doug Davis; all rights reserved