Superposed vibrations with unrelated frequencies never repeat their overall shape

Evidence

Exciting more than one mode by plucking will create a shape distinct from any of the “pure mode” shapes discussed earlier. Each excited mode oscillates sinusoidally, but since they have different frequencies the modes are combining with a relative phase of their respective oscillations that is continuously changing over time. As a result, the shape taken by the two beads changes with time. The two pure mode frequencies are not simply related to each other, and as a result the combined choreography of the beads after such a “pluck” is not periodic. — Eric J. Heller, Why You Hear What You Hear- An…, 786