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An air track supports a cart on a cushion of air to reduce contact friction. It provides a nearly one-dimensional platform for a damped harmonic oscillator; residual drag remains part of the baseline damping.

An actual teaching experiment in Arbor Scientific's The Level Air Track uses one glider, an air track, two photogates, and a ruler. Turn on the blower and place the glider near the middle. Adjust the feet until it does not drift when released. Put the photogates at least half a track length apart and align them with the glider's flag. Measure the length $L$ that interrupts the beams. Give a gentle push, let go, and record each beam-blocking time $\Delta t_i$. The readout is the pair of speeds $s_i=L/\Delta t_i$. The worksheet asks how those speeds compare, which forces remain after the push, and which interaction the air track minimizes.^[ref]

The motivating contrast is between a brief push and the subsequent glide. The air cushion reduces contact friction; it does not remove the downward gravitational weight or the upward support force. Similar successive speeds after release are consistent with a small horizontal net external force, rather than with a continuing push. The experiment approximates the zero net external force model over a finite track and observation interval.

To strengthen the documented procedure, use independent measurement calibration: check the flag length and each timer against a known length and time reference; measuring $L$ sets the length scale but does not calibrate the timer. Repeat launches in both directions without contact during the timed passage, and check for drift at several track locations. These are additional controls, not reported steps or measured results in the worksheet. A residual inclined plane produces a downhill component of gravitational weight with the same laboratory direction on both runs; friction and drag force oppose the direction of travel. Reversing the launch can therefore help distinguish these effects.

A photogate directly measures a beam-blocking time; $L/\Delta t_i$ is an average speed during that passage, not an exact instantaneous velocity. Assign the direction separately. Equal readings at two gates do not prove zero acceleration everywhere between them: opposing changes could cancel. Measurement uncertainty from timer resolution, an incorrectly measured flag length, residual slope, airflow disturbances, and remaining friction or drag force limit the inference. No measured glider speeds are assumed here.

An experimentally useful question is whether the disappearing oscillation follows viscous damping, and whether increasing the brake changes $b$ rather than $m$ or $k$. A published teaching protocol uses a cart on an air track, attached between two springs, with ceramic magnets providing eddy-current damping and an ultrasonic motion sensor recording position against time. Replace the magnets with equal masses in the baseline trial so the moving mass stays fixed. Obtain each spring constant from the slope of applied force versus extension, then use $k=k_1+k_2$. Time many baseline cycles to check ${\omega }_0\simeq \sqrt{k/m}$. Compare one-magnet and two-magnet free decays; the protocol calls for a fit of the full trace including its offset. ^[ref]

The following additional controls make the inference testable. Level the air track and hold its air supply fixed. Check the ultrasonic motion sensor at several stationary flag positions against a ruler, including the full planned travel range; record the offset and scale correction. Check elapsed acquisition time against an independent clock, and choose a sampling rate that resolves many samples within the shortest expected oscillation period. Record the resting equilibrium before and after each run. Release the cart from a small measured displacement with minimal initial velocity, with the driving apparatus inactive. Repeat at several release sizes and magnet settings while keeping the springs and total mass unchanged. These are proposed calibration and repeatability checks, not reported measurements from the source.

For underdamping, fit the recorded position to $y(t)=y_{\mathrm{eq}}+A{e}^{-\alpha t}\cos ({\omega }_{\mathrm{d}}t+\varphi )$ by nonlinear regression. The readout to inspect is a sequence of alternating extrema about $y_{\mathrm{eq}}$ with shrinking amplitudes, and the deviations of the fitted curve from the recorded points. The model predictsCompare the right-hand side, determined independently from mass and spring constants, with the fitted left-hand side. A good fit supports a constant-coefficient single normal mode over the observed range; it does not establish a universal microscopic force law. The published protocol denotes the decay rate by $b$ and the velocity-proportional coefficient by $c$; here they are $\alpha$ and $b$, respectively.

At critical damping or overdamping, fit the corresponding nonoscillatory response including its offset and both initial conditions, rather than forcing a damped cosine onto the data. Adjusting the brake can explore the transition, but the cited protocol does not establish that its one-magnet or two-magnet settings attain critical damping. A near-critical trace over a short interval can be hard to distinguish from neighbouring damping ratios.

Important limitations are finite sensor range, missed or reflected acoustic wave pulses, measurement noise near equilibrium, nonzero release velocity, and position-dependent magnetic braking. Changing the release size tests for quadratic drag or nonlinear spring response; inspecting deviations near turning points can expose kinetic friction. Slow drift of the offset can imitate a long overdamped tail. Report uncertainties in fitted rates and independently measured $m,k$; absence of a visible crossing only bounds the behaviour within the instrument's sensitivity and recording interval. No numerical experimental results are asserted here.

An ultrasonic motion sensor estimates distance from the return delay of an acoustic wave pulse reflected by a target. The teaching setup places a flat flag on the cart facing the detector above the air track, and specifies a minimum range of about $0.3\mathrm{m}$ for its detector. That apparatus-specific limit should not be assumed for every sensor model. ^[ref]