Simple harmonic motion
Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped.The motion is periodic and can be described as that of a sine function, with constant amplitude. It is characterised by its amplitude and its period.
A motion with period T has frequency .
Its importance is that it can serve as a mathematical model of a variety of systems and provides the basis of the characerisation of more complicated motions through the techniques of Fourier analysis.
Simple harmonic motion can in some cases be considered to be the one-dimensional projection of two-dimensional circular motion.
The pulsation is the angular velocity of the corresponding circular motion. Therefore, a motion with period T and frequency has pulsation .
Keep in mind that in general pulsation is not angular velocity. For instance the pulsation of a pendulum is different from its angular velocity. Pulsation is the angular velocity of a circular motion whose projection can be superimposed on the pendulum.
Simple harmonic motion is a good approximation to the motion of a pendulum when the amplitude of the oscillations is small and the mass of the pendulum describes an almost straight line.