Four systems.
One question.
Where does the model stop matching reality?
Begin with the springSpringHooke’s Law
A linear model that works — until it doesn’t.
Drag the free end to stretch ↔
- Extension
- 0.072 m
- Model prediction
- 3.600 N
- Illustrative response
- 3.600 N
- Deviation
- 0.0%
Educational response · k = 50 N/m. Departure is illustrative and does not establish yield. Open Analysis for measured evidence.
PendulumSmall-Angle Approximation
Small angles are powerful. But “small” has limits.
Undamped educational oscillation · swing between ± starting angle
- Angle
- 28.0°
- Small-angle period
- 2.006 s
- Finite-amplitude period
- 2.037 s
- Difference
- +1.51%
Idealized undamped pendulum · L = 1 m · g = 9.80665 m/s². Motion is illustrative; periods use the existing finite-amplitude formula. Open Analysis for measured evidence.
Beer–LambertConcentration Response
Absorbance is approximately linear — within a range.
Incoming light → solution → transmitted light
- Concentration
- 0.45 mmol/L
- Model prediction
- 0.558
- Illustrative response
- 0.558
- Deviation
- 0.0%
Synthetic fixed-path calibration · absorbance is dimensionless. Open Analysis for measured evidence.
Sensor CalibrationLinear Range
Linear response is a design goal. Not a guarantee.
Input movement illustrates a generic response
- Applied input
- 6.2 N
- Expected output
- 1.650 V
- Observed output
- 1.628 V
- Deviation
- -1.3%
Synthetic sensor response · compression does not identify a physical mechanism. Open Analysis for measured evidence.