A single clock can drive two coordinates. The result is a path, not necessarily a function of x.
WHAT HAPPENS IF…Set both frequencies to 1 and phase φ = π/2. Which path appears?
Interactive exploration
Preparing your experiment…
Connect the picture to the ideax(t)=sin(mt+φ),y(t)=sin(nt)
Each t produces a point (x(t), y(t)). Different frequencies m and n and phase φ change the shape. Integer frequencies make the path repeat over 0 to 2π. Faint neighboring curves compare nearby phase shifts.
A detail that matters
A parametric path may pass a vertical-line test or fail it. It is still a valid curve.