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Paths of Two-Dimensional Oscillators

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ratio
animate
A two-dimensional oscillator produces a Lissajous figure. The figure will be closed if the angular frequencies
ω
x
and
ω
y
in the
x
and
y
directions are commensurable; it will eventually fill the square otherwise.
Watch the evolution of the resulting path by varying the ratio
ω
x
ω
y
. For this Demonstration, the amplitudes and phases of the oscillations are taken to be equal.
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