PUZZLE #4226: Resonant Cascade (diff 7)
A damped harmonic oscillator at f0=4.27 Hz, gamma=0.04. Each driving frequency either collapses (A > 4.78) or survives. The collapse pattern encodes the answer.
DATA
| F0 |
4.27
|
| Gamma |
0.04
|
| A Drive |
1.0
|
| A Max |
4.78
|
| Frequencies |
4.27, 9.27, 4.27, 9.27, 9.27, 9.27, 4.27, 9.27, 9.27, 9.27, 9.27, 9.27, 4.27, 9.27, 4.27, 4.27, 9.27, 9.27, 4.27, 9.27, 9.27, 4.27, 4.27, 9.27, 4.27, 9.27, 4.27, 4.27, 4.27, 4.27, 9.27, 9.27, 9.27, 9.27, 4.27, 9.27, 9.27, 9.27, 4.27, 4.27, 9.27, 4.27, 4.27, 4.27, 4.27, 4.27, 9.27, 4.27, 9.27, 4.27, 4.27, 9.27, 9.27, 4.27, 4.27, 4.27, 9.27, 4.27, 9.27, 9.27, 9.27, 4.27, 9.27, 9.27, 4.27, 9.27, 9.27, 9.27, 4.27, 4.27, 4.27, 9.27, 4.27, 9.27, 9.27, 9.27, 4.27, 4.27, 4.27, 4.27, 9.27, 4.27, 4.27, 9.27, 4.27, 9.27, 4.27, 4.27, 4.27, 4.27, 9.27, 9.27, 4.27, 4.27, 4.27, 4.27, 9.27, 9.27, 4.27, 9.27, 9.27, 9.27, 9.27, 9.27, 4.27, 4.27, 9.27, 9.27, 9.27, 9.27, 9.27, 4.27, 9.27, 9.27, 9.27, 4.27, 4.27, 9.27, 9.27, 4.27
|
| Mode |
Resonant Cascade: compute A(f) = A_drive / sqrt((1 - (f/f0)^2)^2 + (2*gamma*f/f0)^2)
|
| Hint |
Oscillator: f0=4.27 Hz, gamma=0.04, A_drive=1.0, A_max=4.78. Compute A(f) for each frequency. Collapse->1, Safe->0. 5-bit groups -> letters. Answer is a 24-letter word.
|
| Answer Format |
lowercase word, no spaces or punctuation
|
author's note: Pool fill: resonant-cascade diff 7
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