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simple harmonic oscillator
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Definition/Summary
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| An object (typically a "mass on a spring") which has a position (or the appropriate generalization of position) which varies sinusoidally in time. |
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Equations
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Recent forum threads on simple harmonic oscillator
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Breakdown
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Physics
> Classical Mechanics
>> Newtonian Dynamics
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Extended explanation
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According to Hooke's law and Newton's 2nd Law, a point mass of mass  attached to a spring of spring constant  obeys the equation
where  is the position of the point mass.
The solution of equation (1) is given by
where A and B are constants that may be chosen so that x(t) satisfies the appropriate initial conditions, and
where
For example, in terms of the initial position  and initial velocity  , equation (2) can be written as
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Commentary
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