Forced Vibration / Resonance Response Calculator mechanism

Model scope

The magnification-factor and displacement-amplitude equations are standard for a harmonically forced, viscously damped, linear single-degree-of-freedom system once omega_n and zeta are defined. The specification fails validation because the phase expression is not quadrant-safe and the resonance-warning behavior and input constraints are unspecified.

• The standard definitions of natural frequency and damping ratio are omitted: omega_n=sqrt(k/m) and zeta=c/(2sqrt(km)). They are required to evaluate r and MF from the listed inputs.
• The phase formula should use atan2(2*zeta*r,1-r^2), not a single-argument atan. For r>1, ordinary atan returns the wrong quadrant and therefore the wrong physical phase.
• The resonance warning has no defined criterion. It should specify whether it warns at r=1, near the damped resonance peak, or according to a configurable tolerance.
• The formula is singular for an undamped system at r=1: zeta=0 and r=1 produce MF division by zero. Required constraints and handling are not specified.

Units and conventions

• F0 is force amplitude in N.
• k is translational stiffness in N/m.
• m is mass in kg.
• c is viscous damping coefficient in N*s/m.
• omega is forcing angular frequency in rad/s, not frequency in Hz; if frequency is supplied in Hz, convert with omega=2*pi*f.
• omega_n=sqrt(k/m) has units rad/s, with radians treated as dimensionless.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "F0_N": 100,
    "k_N_per_m": 10000,
    "m_kg": 1,
    "c_Ns_per_m": 20,
    "omega_rad_per_s": 80
  },
  "expected_outputs": {
    "omega_n_rad_per_s": 100,
    "zeta": 0.1,
    "r": 0.8,
    "MF": 2.53837,
    "X_m": 0.0253837,
    "phase_rad": 0.418224,
    "phase_deg": 23.9625,
    "sampled_plot_point": {
      "x_r": 0.8,
      "y_MF": 2.53837
    },
    "curve_features": {
      "r_at_damped_MF_peak": 0.989949,
      "maximum_MF": 5.02519,
      "MF_at_r_0": 1,
      "MF_as_r_tends_to_infinity": 0,
      "phase_at_r_0_rad": 0,
      "phase_as_r_tends_to_infinity_rad": 3.14159
    }
  },
  "working": "omega_n=sqrt(k/m)=sqrt(10000/1)=100 rad/s. zeta=c/(2sqrt(km))=20/(2sqrt(10000*1))=20/200=0.1. r=omega/omega_n=80/100=0.8. 1-r^2=1-0.8^2=0.36. 2*zeta*r=2*0.1*0.8=0.16. Denominator=sqrt(0.36^2+0.16^2)=sqrt(0.1296+0.0256)=sqrt(0.1552)=0.393954. MF=1/0.393954=2.53837. F0/k=100/10000=0.01 m. X=0.01*2.53837=0.0253837 m. phase=atan2(0.16,0.36)=0.418224 rad=23.9625 degrees. For zeta=0.1, the damped MF peak is at r=sqrt(1-2*zeta^2)=sqrt(0.98)=0.989949, with MF_peak=1/(2*zeta*sqrt(1-zeta^2))=1/(0.2*sqrt(0.99))=5.02519."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument has an unhandled undefined-input failure at k=0: omega_n, zeta, r, MF, phi, and X involve zero denominators or undefined expressions. It should reject the input explicitly. The phase formula also has a quadrant hazard across r=1 if implemented with one-argument atan instead of atan2.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json