Coupled oscillators barely interact when their natural frequencies differ greatly

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

Categorization

• DEFINE: Explains the concept of coupled normal modes and why frequency mismatch suppresses coupling.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 1032
• XREF: connects to: Coupled-oscillator energy sloshing causes the cello’s notorious wolf tone — Eric J. Heller, Why You Hear What You Hear- An…, 1022; Coupled oscillators trade energy back and forth, creating audible beating; Modal coupling factors and resonance frequencies are independently manipulable tools

Broader Connections

• Modal coupling factors and resonance frequencies are independently manipulable tools #corroborates (0.85)