Out-of-phase coupled motion stiffens a system while in-phase motion softens it

Evidence

The reason the frequency of the high mode goes even higher can be seen in the chart graphs. Refer to the green dashed horizontal lines. The higher mode always has the two pendula pushing or pulling against each other, so the effect is a stiffer force because of the spring connecting them. The lower uncoupled frequency goes even lower than the test frequency because the pendula swing together (in phase), which reduces the effect of the spring and lowers the stiffness felt by each oscillator. — Eric J. Heller, Why You Hear What You Hear- An…, 1034

Categorization

• DEFINE: Explains the mechanism behind frequency splitting in coupled oscillators via effective stiffness changes.
• XREF: Connects to acoustics—why coupled resonators/rooms split resonance frequencies.