This simulation generates Lissajous curves by combining two harmonic oscillations with adjustable frequencies and phase differences. Learners manipulate amplitude, frequency ratios, and phase parameters in real time to observe how these variables shape elegant geometric patterns, deepening understanding of parametric equations and periodic phenomena.
Learning objectives: Understand how frequency ratios and phase shifts create different Lissajous patterns | Explore the relationship between parametric equations and visual representations | Investigate harmonic motion and interference effects in two dimensions
Lissajous curves: x = amplitude * cos ( frequency1 * time ) y = amplitude * cos ( frecuency2 * time + phase )
Alfonso Urquía; Carla Martín; Tan Wei Chiong; Loo Kang Wee
license.