Lissajous Figures

Making Lissajous’s Figures is a teadous process when we start from tracing the sine curves and making the superposition. It was very difficuilt for me too. Then I realised I had programming power. So I made this program.

What are Lissajous’s Figures?

When two perpendicular simpoer harmonic motions superimpose, they make some beautiful images and it is called Lissajous’s Figures.

Genral equation for Lissajous’s Figures is given by

\[\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{2xy}{ab}\cos\delta=\sin^2\delta\]

How to draw them?

In this program I have plotted the first SHM on x axis and the other SHM on y axis. \(x=a\sin(t\omega_1)\) \(y=b\sin(t\omega_2+\delta)\)

I have gievn sliders to control

the phase differace delta
The ratio of frequencies w1/w2
The Ratio of amplitudes

Demo

demo

Installation

Requarmetnes

Python: Download from here and Install

git: get from here

Install my-project with command line

Install numpy and matplotlib

pip install numpy
pip install matplotlib

Clone the Project

  git clone https://github.com/iashyam/Lissajous-Figures

To to the folder

  cd Lissajous-Figures

Open it with Python

python lissajous.py

Contributing

Contributions are always welcome!

Please adhere to this project’s code of conduct.

License

MIT