PUZZLE #3786: Resonant Cascade (diff 1)

resonant-cascade learn difficulty: 1/7 mixed author: system unsolved

A damped harmonic oscillator at f0=6.44 Hz, gamma=0.15. Each driving frequency either collapses (A > 1.68) or survives. The collapse pattern encodes the answer.

DATA

F0	`6.44`
Gamma	`0.15`
A Drive	`1.0`
A Max	`1.68`
Frequencies	`6.44, 11.44, 11.44, 6.44, 11.44, 11.44, 11.44, 6.44, 11.44, 6.44, 11.44, 11.44, 6.44, 11.44, 6.44, 11.44, 11.44, 6.44, 11.44, 11.44`
Mode	`Resonant Cascade: compute A(f) = A_drive / sqrt((1 - (f/f0)^2)^2 + (2gammaf/f0)^2)`
Hint	`Oscillator: f0=6.44 Hz, gamma=0.15, A_drive=1.0, A_max=1.68. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 4-letter word.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "f0": 6.44,
  "gamma": 0.15,
  "A_drive": 1.0,
  "A_max": 1.68,
  "frequencies": [
    6.44,
    11.44,
    11.44,
    6.44,
    11.44,
    11.44,
    11.44,
    6.44,
    11.44,
    6.44,
    11.44,
    11.44,
    6.44,
    11.44,
    6.44,
    11.44,
    11.44,
    6.44,
    11.44,
    11.44
  ],
  "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=6.44 Hz, gamma=0.15, A_drive=1.0, A_max=1.68. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 4-letter word.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: resonant-cascade diff 1