Lissajous Figures Lissajous curves were studied by the French physicist and mathematician Jules Antoine Lissajous (1822 - 1880). Lissajous curves are the composition of two harmonic motions (sinusoids):

x = amplitude * cos ( frequency1 * time )
y = amplitude * cos ( frecuency2 * time + phase )
The shape of the curves are highly sensitive to the ratio frequency1/frequency2. Do experiment with different values of the frequencies and the phase using the fields provided in the simulation. Activities This virtual-lab will enable you to analyze the Lissajous figures. The view of the virtual-lab contains three buttons (A, B and C), which set predefined values to the frequency and the phase of the harmonic signals. In addition, the numerical values of the frequency and the phase can be selected by the lab's user. Authors Alfonso Urquía and Carla Martín
Dpto. de Informática y Automática
E.T.S. Ingeniería Informática, UNED
Juan del Rosal 16, 28040 Madrid, Spain

### Software Requirements

SoftwareRequirements

 Android iOS Windows MacOS with best with Chrome Chrome Chrome Chrome support fullscreen? Yes. Chrome/Opera No. Firefox/ Sumsung Internet Not yet Yes Yes cannot work on some mobile browser that don't understand JavaScript such as..... cannot work on Internet Explorer 9 and below

### Credits

Alfonso Urquía; Carla Martín; Tan Wei Chiong; Loo Kang Wee

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### For Teachers

Lissajous curves are a family of parametric curves studied by the French physicist and mathematician Jules Antoine Lissajous (1822 - 1880).

Lissajous curves are the composition of two harmonic motions (sinusoids):
x = amplitude * cos ( frequency1 * time )
y = amplitude * cos ( frecuency2 * time + phase )

The shape of the curves are highly sensitive to the ratio frequency1/frequency2.
There are 3 curves A, B, and C in this simulation, which are vastly different from each other. The amplitude of the curve is set to 30, but both frequencies and the phase can be changed.

Do experiment with different values of the frequencies and the phase using the fields provided in the simulation, and see how the graph changes.

Research

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### Version:

1. http://weelookang.blogspot.sg/2016/02/vector-addition-b-c-model-with.html improved version with joseph chua's inputs
2. http://weelookang.blogspot.sg/2014/10/vector-addition-model.html original simulation by lookang

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