Hooke's Law Spring Bench (2D)

Hang masses on a damped spring, read a noisy ruler, and fit the spring constant with an uncertainty. Same solver as the 3D bench.

Live readout

Numerical checks

The science

A mass on a spring obeys m x'' = m g - k x - c x', settling to x = m g / k (here k = 12 N/m). Each reading is the settled extension with ruler noise (0.6 mm, 1 mm rounding) and scale noise; k is the least-squares slope of force vs extension, with a Student-t small-sample uncertainty.

Guide friction (0.04 N) makes the spring stick short of equilibrium, extra drag only slows the settling, a parallax error stretches every reading by 4 % and biases k low: systematic errors do not average out.
The simplification: an ideal linear spring with no mass of its own and no hysteresis.

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