Coupled oscillators trade energy back and forth, creating audible beating

Evidence

If we set both pendula free (but they are still coupled by the spring), for any given length of the red oscillator, there are two new purely sinusoidal (pure) modes, each with a distinct frequency, and each involving the sinusoidal motion of both oscillators at that frequency. However, if the test frequencies of the red and blue pendula alone are very different, the two pendula don’t interact very much, in spite of the spring connecting them. One mode will be mostly red pendulum motion at a frequency just above the red-only test frequency. Another will be mostly blue pendulum motion at a frequency just below the blue-only test frequency. Note that the lower frequency uncoupled mode is always pushed still lower, and the higher one a bit higher, compared to the individual test frequencies. Starting at rest, hitting one or the other of the pendulum oscillators will excite both of the modes, and the motion will consist of the superposition of two sinusoidal motions of (typically) incommensurate frequency. — Eric J. Heller, Why You Hear What You Hear- An…, 1032 (#qualifies, via linked claim)

Categorization

• XREF: connects to: Piano strings and soundboards can exchange energy producing audible loudness shimmer; Coupled-oscillator energy sloshing causes the cello’s notorious wolf tone — Eric J. Heller, Why You Hear What You Hear- An…, 1022; Coupled oscillators barely interact when their natural frequencies differ greatly — Eric J. Heller, Why You Hear What You Hear- An…, 1032 (+2 more)

Related

• Coupled oscillators barely interact when their natural frequencies differ greatly (similarity 0.91)
• Near-resonant coupled oscillators mix their motion into two equal hybrid modes (similarity 0.82)
• Coupled string and board modes produce wavering sound rather than steady tone (similarity 0.81)
• Out-of-phase coupled motion stiffens a system while in-phase motion softens it (similarity 0.81)
• Coupled oscillators underpin most heard sound production (similarity 0.80)
• Piano strings and soundboards can exchange energy producing audible loudness shimmer (similarity 0.80)
• Two coupled modes split above and below the test frequency, causing beat frequencies (similarity 0.80)
• Coupled oscillator modes smoothly trade character as one natural frequency passes the other (similarity 0.80)
• Coupled-oscillator energy sloshing causes the cello’s notorious wolf tone (similarity 0.80)
• Oscillatory click responses arise from phase-locked spikes separated by one period of best frequency (similarity 0.80)
• Impacting one coupled bead excites two incommensurate modes whose sum is non-periodic (similarity 0.78)

Broader Connections

• Two coupled modes split above and below the test frequency, causing beat frequencies #expands (0.90)
• Coupled oscillators barely interact when their natural frequencies differ greatly #qualifies (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 1032
• Oscillatory click responses arise from phase-locked spikes separated by one period of best frequency #exemplifies (0.75)