| Simple Harmonic Motion |
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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 is the phase of oscillation. If there is no displacement at time t = 0, the phase . A motion with frequency ''f'' has Period . 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 attached to a spring of spring constant 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 class="copylinks">Projection Of [[uniform Circular Motion . If an object moves with angular speed around a circle of radius centered at the Origin of the '''x-y''' plane, then its motion along the '''x''' and the '''y''' coordinates is simple harmonic with amplitude and angular speed . Pendulum: In the Small Angle Approximation , the motion of a pendulum is simple harmonic motion. SEE ALSO |
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