Resonance occurs when the driving force and velocity align in phase

Evidence

The notion of force (and therefore acceleration) in phase with velocity meshes perfectly with our definition of resonance at the beginning of this chapter. According to Newton’s second law, F = ma, where acceleration a is the rate of change of velocity. If a force F is applied for a time Δt, the velocity changes by Δν = aΔt = (F/m)Δt; the new velocity is ν′ = υ + Δυ. If the initial velocity υ is positive and the force F is also positive, the additional velocity Δυ is positive too, resulting in constructive interference—that is, resonant addition of velocity amplitude. The same is true if force and velocity are negative, reinforcing the negative velocity. — Eric J. Heller, Why You Hear What You Hear- An…, 993

Categorization

• DEFINE: Explains the mechanism by which in-phase force and velocity produce constructive interference — the conceptual root of resonance.