Free Vibration

x(t) = x(t+T)

Simple harmonic motion is often represented as the projection on a straight line of a point that is moving on a circle at constant speed. With the angular speed of the line OP designated by , the displacement x(here vertical diameter is treated as x-axis) can be written as,

The acceleration is

Thus, a characteristic of simple harmonic motion is that the acceleration is proportional to displacement pointing opposite to the displacement.