# Classical Motion and Phase Space for a Harmonic Oscillator

Classical Motion and Phase Space for a Harmonic Oscillator

This Demonstration illustrates the classical harmonic motion of a particle governed by the Hamiltonian , where the scaled variables are defined as ≡, ≡. Here (t) and (t) are obtained by solving Hamilton's equations of motion, subject to the initial conditions =(0) and =(0). The three panels animate synchronously: (1) the motion of the particle in the potential; (2) the phase space trajectory; and (3) the time series of (t) and (t). In the upper two panels, the points with minimum (turning points) and maximum momentum are labeled with blue and green 's, respectively.

H=+

ω

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2

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2

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mω

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mω

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0

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0

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