Lissajous Curves

Lissajous curves are complex, symmetrical patterns formed when two oscillating signals, typically sine waves, are combined at right angles. Imagine swinging two pendulums, one horizontal and one vertical, with different frequencies; the path they create together is a Lissajous curve. These patterns depend on the frequency and phase difference between the waves. They’re visual representations often seen on oscilloscopes, illustrating the relationship between two vibrating signals. Despite their intricate appearance, they represent simple harmonic motions and are used in physics, engineering, and art to analyze and visualize wave interactions.