PUZZLE #4222: Resonant Cascade (diff 2)

resonant-cascade learn difficulty: 2/7 mixed author: system unsolved

A damped harmonic oscillator at f0=4.22 Hz, gamma=0.12. Each driving frequency either collapses (A > 1.56) or survives. The collapse pattern encodes the answer.

DATA

F0	`4.22`
Gamma	`0.12`
A Drive	`1.0`
A Max	`1.56`
Frequencies	`4.22, 9.22, 4.22, 9.22, 9.22, 4.22, 9.22, 9.22, 4.22, 9.22, 9.22, 9.22, 4.22, 9.22, 4.22, 9.22, 4.22, 4.22, 9.22, 4.22, 9.22, 9.22, 9.22, 4.22, 9.22, 9.22, 4.22, 4.22, 9.22, 9.22, 9.22, 9.22, 4.22, 9.22, 4.22`
Mode	`Resonant Cascade: compute A(f) = A_drive / sqrt((1 - (f/f0)^2)^2 + (2gammaf/f0)^2)`
Hint	`Oscillator: f0=4.22 Hz, gamma=0.12, A_drive=1.0, A_max=1.56. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 7-letter word.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "f0": 4.22,
  "gamma": 0.12,
  "A_drive": 1.0,
  "A_max": 1.56,
  "frequencies": [
    4.22,
    9.22,
    4.22,
    9.22,
    9.22,
    4.22,
    9.22,
    9.22,
    4.22,
    9.22,
    9.22,
    9.22,
    4.22,
    9.22,
    4.22,
    9.22,
    4.22,
    4.22,
    9.22,
    4.22,
    9.22,
    9.22,
    9.22,
    4.22,
    9.22,
    9.22,
    4.22,
    4.22,
    9.22,
    9.22,
    9.22,
    9.22,
    4.22,
    9.22,
    4.22
  ],
  "mode": "Resonant Cascade: compute A(f) = A_drive / sqrt((1 - (f/f0)^2)^2 + (2*gamma*f/f0)^2)",
  "note": "For each frequency, collapse = amplitude > A_max (bit=1). Group bits in 5, map 00001=A..11010=Z.",
  "hint": "Oscillator: f0=4.22 Hz, gamma=0.12, A_drive=1.0, A_max=1.56. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 7-letter word.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: resonant-cascade diff 2