Lissajous Curve Parametric Plot

This GeoGebra example dynamically constructs Lissajous curves using parametric equations, visualizing the superposition of two harmonic oscillations with adjustable frequency ratio, amplitude, and phase difference. The construction employs GeoGebra commands such as Intersect, Locus, and slider-controlled parameters (a, b, α, δ) to generate the curve’s locus in real time. It serves as an excellent resource for high school and early college mathematics, trigonometry, and physics courses exploring parametric functions, wave interference, and geometric loci. Users can interactively modify frequency and phase parameters to observe how the resulting curve transitions between simple ellipses and complex rosette patterns.