812 Lissajous Figures on CRO

When the CRO is set to the xy mode, it uses the Channel 1 input as the time-base. This means the x and y position of the CRO trace is controlled by inputs from Channel 1 and 2 respectively.

If both channels are fed with sinusoids with the same frequency, then the following traces wil result, depending on the phase relationship between the two sinusoids.

Picture1

In-phase. Much like the relationship between force and acceleration.

Picture2

Anti-phase. Much like the relationship between acceleration and displacement for a SHM.

Picture3

A quarter-cycle out of phase. Much like velocity leading displacement for a SHM.

In this demo, because I was using analogue signal generators, I was unable to set the inputs to the exact frequencies I wanted. So even though I was aiming for 100 Hz for both channels, I could only get them to be close to but not exactly 100 Hz. This means there was a slight difference in the periods of the two signals. This causes their phase relationship to keep shifting, alternating between in-phase and anti-phase. This results in the lovely outcome of the tracing alternating between diagonals and flipped diagonals, including the ellipses between.

When Channels 1 and 2’s frequencies are a nice integer ratio of each other, very intricate patterns are formed. By counting the number of times the trace cuts each axis, one can figure out the exact ratios. If you are interested and want to read up more, just google “Lissajous Figures”.

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