Spring-Mass SHM Calculator mechanism

Model scope

The position and velocity formulas are correct under the stated ideal-SHM assumptions. The specification is not complete enough to pass because acceleration, period, and frequency formulas are omitted even though those quantities are advertised, and phase units and plotting behavior need explicit constraints.

• The listed formulas for angular frequency, position, and velocity are standard for an undamped ideal mass-spring oscillator, provided k>0, m>0, and phase is in radians.
• Acceleration is an advertised output but its formula is missing. It should be a(t)=-Aω²cos(ωt+φ)=-ω²x(t).
• Period and frequency are advertised outputs but their formulas are not listed. They should be T=2π/ω=2π√(m/k) and f=1/T=ω/(2π).
• The plotted quantity and curve-feature definitions are underspecified: the instrument should state whether it plots x, v, and a versus time on separate axes or a shared axis, and should define the plotted time interval and sampling behavior.

Units and conventions

• k is positive spring stiffness in N/m.
• m is positive mass in kg.
• A is displacement amplitude in m; normally A≥0.
• time t is in seconds.
• φ is a phase angle in radians, dimensionless; degrees must not be silently accepted as radians.
• ω is in rad/s, T is in s, f is in Hz, x and A are in m, v is in m/s, and a is in m/s².

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "k": 100,
    "m": 1,
    "A": 0.2,
    "phi_rad": 0,
    "time_s": 0
  },
  "expected_outputs": {
    "omega_rad_per_s": 10,
    "period_s": 0.628318531,
    "frequency_hz": 1.59154943,
    "x_m": 0.2,
    "v_m_per_s": 0,
    "a_m_per_s2": -20,
    "key_curve_features": {
      "x_roots": "t=(π/2+nπ)/10 s",
      "x_max": "x=+0.2 m when 10t=2πn",
      "x_min": "x=-0.2 m when 10t=(2n+1)π",
      "v_extrema": "v=±2 m/s",
      "a_extrema": "a=±20 m/s²",
      "asymptotes": "none"
    }
  },
  "working": "ω=√(k/m)=√(100/1)=10 rad/s. T=2π/ω=2π/10=0.628318531 s. f=1/T=10/(2π)=1.59154943 Hz. At t=0, θ=ωt+φ=10(0)+0=0. x=A cosθ=0.2 cos0=0.2 m. v=-Aω sinθ=-(0.2)(10)sin0=0 m/s. a=-Aω²cosθ=-(0.2)(10²)cos0=-20 m/s²."
}

Failure boundary

• Division by zero or invalid square root occurs if m≤0; k≤0 is also invalid for the claimed ordinary oscillatory SHM model.
• A negative amplitude is mathematically redundant because its sign can be absorbed into φ; the input contract should require A≥0 or normalize the phase.
• Phase-unit ambiguity can cause a major error if degrees are supplied where radians are expected.
• The acceleration output cannot be verified from the listed specification because its formula is omitted.
• Period and frequency are not explicitly defined in the formula list despite being advertised outputs.
• The instrument should state how many time samples are plotted, the time range, and whether numerical rounding or adaptive sampling is used.
• For an ideal oscillator, there are no asymptotes; any displayed asymptote or damping behavior would contradict the honest label.

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