Page 7

LISSAJOUS FIGURES

Lissajous figures are created when a parametric plot (see below) is made of y vs x, when both y and x are sinusoidally varying functions of time, that is x=xocos(w1t) and y=yocos(w2t). When the two frequencies are related to each other as the ratio of two integers (an example of resonance) a stable plot is obtained. An oscilloscope is a useful tool for displaying these traces, since one setting of the time-base control allows the horizontal axis to be controlled by an applied voltage, rather than by the time-base of the oscilloscope itself.

In this demonstration, the figure to the left represents an oscilloscope screen in which the horizontal axis has been changed from a time-base to a second voltage. Both axes are being driven by sinusoidally varying voltages. They have frequencies which are multiples of each other, but with a variable phase between the two. For this we can write:

V1 = Vo sin(w1t)
V2 = Vo sin(w2t + d)

You can choose the ratio of the two frequencies by selecting from the table to the left, and vary the relative phase by using the scroll bar below the oscilloscope screen.

1

2

3

4

5

w 1

1

2

3

4

5

w2

In order to see this you nee a Java
compatible browser.

Making Lissajous Figures
Lissajous figures are not difficult to make on the oscilloscope. You will need two function generators, one connected to channel A and the other to channel B. Turn the time-base control fully clockwise until it reads X. If you adjust the frequency of one of the function generators you should be able to generate all of the pictures above, and many more. Note the trace is only stable if the two frequencies are exactly in the ratio of two integers.
Parametric Plot - comes from the word Parameter.  A parameter is "a value."  A range of Parameters is a range of values.