Resonance perturbation — the 3-step answer
● VERBATIM — examined word-for-word"X changes; what happens to the amplitude?" Always: (1) name what changed → (2) trace it to f_d, f₀ or damping → (3) state the amplitude effect. Worked set (N94 floating block at resonance): bigger incident waves → driver amplitude up → larger amplitude, still at resonance. Crest spacing (λ) increases at same wave speed → f_d = v/λ falls below f₀ → off resonance → amplitude drops. Block absorbs water → m up → f₀ = √(k/m)/2π falls → mismatch (and heavier damping) → amplitude drops. Rotating machinery (washing machine): the imbalanced rotation IS the periodic driver; max amplitude when rev s⁻¹ = f₀ = 1/T.
What this actually means
Every 'X changes, what happens to the amplitude?' question has the same skeleton: name the change, trace it to one of f_d, f₀ or damping, state the amplitude consequence. Three sentences, every time.
The N94 floating block runs the full set. Bigger incident waves: driver amplitude up, response larger, still resonant. Longer crest spacing at the same wave speed: f_d = v/λ falls below f₀, off resonance, amplitude drops. Block absorbs water: m rises, f₀ = √(k/m)/2π falls, mismatch again, amplitude drops.
Rotating machinery is the same skeleton in disguise: the imbalanced rotation IS the periodic driver, so maximum shaking arrives when revolutions per second equal f₀.
Prove it — watch it be true
- Park the system at resonance
- Shift f_d slightly off f₀: amplitude falls — that is the λ-change case
- Instead raise the damping: amplitude falls a different way — trace each change to its lever