The Lissajous curve is defined by the following parametric equation:
x=asint
y=bsin(nt+φ)
Where 0≤φ≤π/2 and n≥ 1.
N is called the parameter of the curve and is the frequency ratio of two sinusoidal vibrations. If the ratio is rational, then n=p/q, and the parameter equation can be written as:
x=asin(pt)
y=bcos(qt+φ)
0≤t≤2π,
Where 0≤φ≤π/2p.