PUZZLE #4218: Resonant Cascade (diff 6)

resonant-cascade learn difficulty: 6/7 mixed author: system unsolved

A damped harmonic oscillator at f0=5.51 Hz, gamma=0.05. Each driving frequency either collapses (A > 5.75) or survives. The collapse pattern encodes the answer.

DATA

F0	`5.51`
Gamma	`0.05`
A Drive	`1.0`
A Max	`5.75`
Frequencies	10.51, 10.51, 5.51, 5.51, 10.51, 10.51, 5.51, 5.51, 10.51, 10.51, 10.51, 10.51, 5.51, 10.51, 5.51, 5.51, 5.51, 10.51, 10.51, 10.51, 10.51, 5.51, 5.51, 5.51, 5.51, 10.51, 10.51, 5.51, 10.51, 5.51, 10.51, 5.51, 5.51, 10.51, 10.51, 10.51, 10.51, 5.51, 10.51, 5.51, 10.51, 10.51, 10.51, 5.51, 5.51, 5.51, 10.51, 5.51, 10.51, 10.51, 5.51, 10.51, 10.51, 5.51, 10.51, 10.51, 5.51, 10.51, 10.51, 5.51, 10.51, 10.51, 10.51, 5.51, 5.51, 10.51, 5.51, 10.51, 10.51, 5.51, 5.51, 10.51, 5.51, 10.51, 10.51, 5.51, 5.51, 10.51, 10.51, 5.51
Mode	`Resonant Cascade: compute A(f) = A_drive / sqrt((1 - (f/f0)^2)^2 + (2gammaf/f0)^2)`
Hint	`Oscillator: f0=5.51 Hz, gamma=0.05, A_drive=1.0, A_max=5.75. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 16-letter word.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "f0": 5.51,
  "gamma": 0.05,
  "A_drive": 1.0,
  "A_max": 5.75,
  "frequencies": [
    10.51,
    10.51,
    5.51,
    5.51,
    10.51,
    10.51,
    5.51,
    5.51,
    10.51,
    10.51,
    10.51,
    10.51,
    5.51,
    10.51,
    5.51,
    5.51,
    5.51,
    10.51,
    10.51,
    10.51,
    10.51,
    5.51,
    5.51,
    5.51,
    5.51,
    10.51,
    10.51,
    5.51,
    10.51,
    5.51,
    10.51,
    5.51,
    5.51,
    10.51,
    10.51,
    10.51,
    10.51,
    5.51,
    10.51,
    5.51,
    10.51,
    10.51,
    10.51,
    5.51,
    5.51,
    5.51,
    10.51,
    5.51,
    10.51,
    10.51,
    5.51,
    10.51,
    10.51,
    5.51,
    10.51,
    10.51,
    5.51,
    10.51,
    10.51,
    5.51,
    10.51,
    10.51,
    10.51,
    5.51,
    5.51,
    10.51,
    5.51,
    10.51,
    10.51,
    5.51,
    5.51,
    10.51,
    5.51,
    10.51,
    10.51,
    5.51,
    5.51,
    10.51,
    10.51,
    5.51
  ],
  "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=5.51 Hz, gamma=0.05, A_drive=1.0, A_max=5.75. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 16-letter word.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: resonant-cascade diff 6