A pen fixed to an object bouncing on a spring draws on a paper strip pulled steadily sideways. What shape does the trace take?

1. The vertical position of the object follows x(t) = X cos(2 pi t / T). 2. Pulling the paper sideways at a steady rate turns the horizontal axis of the trace into a time axis. 3. Plotting a cosine against time draws a smooth sine-shaped wave. 4. A saw-tooth would need an abrupt jump each cycle, which a smoothly turning oscillator never makes. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section The Link between Simple Harmonic Motion and Waves_