Impacting one coupled bead excites two incommensurate modes whose sum is non-periodic

Evidence

Giving all of the energy to one pendulum initially is like hitting one bead of a two-bead system (see figure 8.3 and surrounding discussion). The beads are coupled together by filament, and such an impact will excite both modes of motion, each one periodic with a different frequency. The sum of the two is not periodic, because the frequencies are not commensurate. — Eric J. Heller, Why You Hear What You Hear- An…, 1023