Harmonograph Rainbow: Parametric Curves with Damped Vibrations

① This example demonstrates a rainbow-colored parametric curve generated by the superposition of multiple damped harmonic oscillations, producing intricate spiral and wave patterns reminiscent of a physical harmonograph. ② Core mathematical concepts include parametric equations, simple harmonic motion, damping decay, curve superposition, and limits (as time approaches infinity, the curve converges to a central point). ③ Construction highlights: using GeoGebra's CurveCartesian command, with objects such as b, a, g, f, c, h, p, d, damp (damping function), func (function), para (parameter), and text elements; sliders or text inputs control parameters to animate the rainbow effect. ④ Suitable for high school to university students learning parametric curves, vibration synthesis, and damped motion, as well as for artistic mathematics or fractal geometry extensions.