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Lissajous figures
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Paths from perpendicular SHMs with different frequencies.
Perpendicular oscillations with frequency ratio p:q trace closed curves. Equal frequencies give ellipses, circles or lines depending on phase difference.
An oscilloscope in XY mode displays them.
Used for comparing frequencies.
In more detail
Lissajous figures are curves traced when two perpendicular oscillations with different frequencies combine. Their shape depends on the frequency ratio and phase difference.
Real-world uses
- Oscilloscopes use Lissajous patterns to compare frequencies.
- Physics labs use Lissajous figures to measure phase differences.
- Physicists use Lissajous figures to compare the frequencies of two signals on an oscilloscope.
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Frequently asked questions
What do the shapes tell me?
The frequency ratio sets the number of loops, and the phase difference sets the shape.
What is a simple ratio pattern?
Equal frequencies give ellipses or straight lines, depending on phase.
What does a closed Lissajous figure mean?
The two frequencies are in a simple whole-number ratio, so the pattern repeats after a fixed time.
Related topics in Oscillations & SHM
Normal modes · Beats in oscillators · Superposition of SHMs · Anharmonic oscillation · Nonlinear oscillators · Chaos and the double pendulum