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
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.
V1 = Vo sin(w1t)
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.
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.