Lissajous figures are displays on the oscilloscope screen, which are easy to set

Question

Lissajous figures are displays on the oscilloscope screen, which are easy to set up. Connect a second signal generator to the second input of the oscilloscope. Change the display type of the oscilloscope to X-Y display by pressing the X-Y button. The oscilloscope is now acting as an X-Y plotter. Keeping one output at 600 Hz, adjust the other frequency generator until a simple stable pattern is obtained, without too many loops. Record the frequencies and determine the relationship between the frequencies of the two signals and the number of loops present.

Explanation / Answer

Practically you need to connect one of thefunction generator to x input of oscilloscope and the other function generator to the y input of the oscilloscope. The create a table with column F1, F2, LCM F1,F2 and HCF F1,F2. You'll see a very canonic relationship between these variables. The theoretical part is explained in the following section intuitively. Let us consider that we set the frequencies to be equal. It's the sensible to expect a single loop that can look like a circle or ellipse because both the signals attain the same value after one complete time period. Now if we increase the frequency of one of the scope to twice the other for every time period of the slower scope the faster scope would actually cover two complete cycles hence give us two loops. In general if the two scopes have frequencies nf and mf where n and m are coprime integer multiples of the frequency f then a total of mn loops should be observable because both the signals repeat simultaneously after mn cycles.

Loops of LoopsM(F1, F2)/HCF(F1,F2)

Nber Loopsit helps. You'll definitely appreciate it with an oscilloscope but for practice you can use some simulation tool like MATLAB. All the best.

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