A periodic motion in which the restoring influence acting towards the rest position is proportional to the displacement from rest, as in a pendulum undergoing small swings. Simple harmonic motion is much easier to analyse than general periodic motion; the latter can be broken down into simple harmonic components.
Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped.
One definition of simple harmonic motion is "motion in which the acceleration of the oscillator is proportional to, and opposite in direction to the displacement from its equilibrium position", or .
A general equation describing simple harmonic motion is , where y is the displacement, A is the amplitude of oscillation, f is the frequency, t is the elapsed time, and γ is the phase of oscillation.
Simple harmonic motion can serve as a mathematical model of a variety of motions and provides the basis of the characterisation of more complicated motions through the techniques of Fourier analysis.
Realizations
Simple harmonic motion is exhibited in a variety of simple physical systems and below are some examples:
Mass on a spring: A mass M attached to a spring of spring constant k exhibits simple harmonic motion in space with
Alternately, if the other factors are known and the period is to be found, this equation can be used:
Uniform circular motion: Simple harmonic motion can in some cases be considered to be the one-dimensional projection of uniform circular motion.
Mass on a pendulum: In the small-angle approximation, the motion of a pendulum is shown to approximate simple harmonic motion.
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