In evenly matched systems, the roles of driving and driven swap as energy sloshes

Evidence

We mentioned the difference between autonomous resonance and driven resonance. If Saturn, the shepherding moons, and the ring material are viewed as a closed system, this system is both resonant and autonomous. But the moons are heavy, and the ring material is light. The moons may be taken to be driving the rings externally. In cases where the drive and the driven are more evenly matched, energy sloshes around inside autonomous systems as different parts find themselves frequency and phase matched with other parts. What is driving (losing energy) and what is being driven (gaining energy) switches back and forth. In discussing the damped harmonic oscillator in the next chapter (section 10.7), we will investigate the coupling of two pendula of equal length and thus frequency, connected by a weak spring. Together, the two coupled pendula form an autonomous system. If one of them starts oscillating, it is automatically forcing the other resonantly, and so energy starts to flow from the first to the second pendulum. The resonance causes the energy to slosh back and forth between them, if one of them is initially given a push and the other not, starting at rest. — Eric J. Heller, Why You Hear What You Hear- An…, 932

Categorization

• DEFINE: Clarifies the autonomous vs. driven resonance distinction and shows the two-pendulum model as the canonical illustration.
• XREF: The two coupled pendula prefigure the damped harmonic oscillator treatment promised in the next chapter — useful setup for the mechanics of energy transfer.