A dumb sinusoidal drive self-sets its phase relative to the oscillator

Evidence

The frequency of the drive relative to the natural frequency f0 of the bead or oscillator is of great importance to resonance, but the frequency alone does not specify when the force is applied in the course of an oscillation—that is, the phase of the drive relative to the oscillation. It would therefore seem that achieving resonance is also a matter of controlling the phase of the drive relative to the vibration, not just the frequency. Indeed “smart” drives (like a parent pushing a child on a swing) do need to deliberately time the pushes. But for a strong (noninteractive, typically high-impedance) but “dumb” sinusoidal drive, everything including the relative phase of the drive and the displacement settles down to a steady oscillation at the drive frequency f after about Q oscillations. The phase depends on the amount of friction and the drive frequency relative to the natural system resonant frequencies, as shown in figure 10.4. The phase of a sinusoidal drive of prescribed force sets itself up naturally. The relative phase of the force and the velocity advances by π (180 degrees) in passing from well below to well above resonance. — Eric J. Heller, Why You Hear What You Hear- An…, 984

Categorization

• DEFINE: Clarifies the distinction between ‘smart’ drives that need to time pushes (like pumping a swing) versus ‘dumb’ sinusoidal drives that settle into steady phase automatically.