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Lissajous

by Paul Rieger (Submitted: 12/21/2003)

[screen shot]

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WHAT IS IT?

Plot Lissajous-figures on the screen.
A mass-point is distraced by two forces. One takes effect in the x-direction
the other in the y-direction. These forces are controlled by different
sinusoidal functions and the resolving curve of the mass point is drawn in
the graphics-window.

HOW IT WORKS

An invisible turtle is generated and the position is calculated.
The following positions are visualized while the turtle marks its way in
green color.

HOW TO USE IT

Xfreq, Yfreq: Sliders to adjust the frequency in the x- and y-direction.
The value can be set from 0 to 10 with increments of 0.5
So you can get 10 sine-oscillations in each direction.
Note: The calculation of the angle runs up to 720 degrees for rational numbered values of the frequencies. If you
think that nothing is happening the mass-point may be one
his way back on the same track.
Xphase, Yphase: To set the phase displacement (or zero-crossing) of each
direction.

THINGS TO NOTICE

Please be patient: wait until the "go"-Button turns grey again. (See the
note at Xfreq, Yfreq).
If the ratio Xfreq/Yfreq is whole-numbered you'll get the well known plots.
It's more fun with other combinations.

THINGS TO TRY

First start with whole numbered low frequencies and no phase displacement.
Then change either the Xphase or Yphase in great amounts. After that you
can set the frequencies to "strange" values.
Or try Xfreq = 10.0 and Yfreq = 9.5; both Xphase = Yphase = 0.
Play along and have fun!

EXTENDING THE MODEL

It would be great if the turtle could draw lines between the positions.
Sliders for the magnitude could be added (but that's not really interesting).
The increments of the Xphase/Yphase sliders could be set to 1, if the
calculation of the angle is increased.
A color choice could be added.

CREDITS AND REFERENCES

Jules Antoine Lissajous (*1822 +1880) french physician.

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