Lissajous Curves
Instructions:
Move sliders \(d\) (phase-difference), \(a\) or \(b\) (frequencies) to change the red curve. Press the "Start" button to watch the animation, this will move the \(t\) (time) slider. Press the "Stop" button to interrupt the animation and press the "Reset" button to reboot the starting values.
$$ x = A \sin \left(a t + \delta \pi \right); \; y = B \sin \left(b t \right) $$