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Written By Stephen Wilson

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Lissajoux Figures

Stephen K. Wilson, Oakes, Huddersfield

When two sets of waves produce a geometrical shape a Lissajous figure is created. This program simulates this effect as produced on an oscilloscope screen. With the instrument's time-base off, one oscillating signal is connected to the X plate and one to the Y plate. If the frequencies of these signals are in a simple ratio a recognised symmetrical figure is formed. In physics these figures are used for determination of an unknown frequency through comparison with a known one. The nature of the figure depends on the path different between the signals. With the simplest of all ratios - 1:1 - the figure is a sloping line with a path difference of 0 rads, a sloping ellipse with a path difference of one quarter of the rads, and a circle with a path difference of half of PI.

In this simulation the user is asked to input the ratio of frequencies in lowest terms, and the path difference between the signals - X signal leading Y signal - as a fraction of PI. The computer calculates and draws the figure.

The program will run on either BBC Model, though those with Model Bs would wish to alter line 15 to run it in Mode 0 for greater resolution. Those with greater patience and a greater desire for accuracy might wish to reduce the STEP command at line 100.

With a view to converting to other Basic dialects it is worth mentioning that @% is a formatting feature which displays all figures to two decimal places. The VDU 28 call defines a text window at top-centre screen which is cleared by the VDU 12 call and cancelled with VDU 26, line 95. *FX 15,0 clears the keyboard buffer, line 25.