## simple harmonic motion (SHM)
O, so that its acceleration
towards O is always proportional to its distance from O.
Thus, if a point P moves in a circle,
center O and radius r, with a constant angular
velocity ω, the projection of P on any diameter
will move in simple harmonic motion. If the distance from O of
the projection of P on a vertical diameter is y, at time
t, then a graph of y against t will give a sine
wave of amplitude r and equation
y = r sinωt. This equation may be rewritten
in the more general form: y = r sin2π(t /T - x/λ)
where T is the period of the wave,
λ its wavelength and
x the distance it has traveled from O in time t.
Simple harmonic motion derives its name from the fact that the vibrations produced by musical instruments (e.g., a string of a violin, the legs of a tuning fork), and hence the sound waves they propagate, approximate to it. In fact these, as all other vibrations and wave motions, may be treated as compounded of a number of SHMs. ## Related categories• CLASSICAL MECHANICS• WAVES AND WAVE PHENOMENA | ||||||||

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