Forced Oscillator: Natural Frequency from the Resonance Peak

A hidden driven oscillator. Sweep drive frequency, find the amplitude peak, and report that ω as ω₀.

University / research· 22 min·Related simulator: Classical MechanicsForced Oscillator

Goal

Determine ω₀ as the drive frequency of maximum steady amplitude. Light damping makes ω_res ≈ ω₀.

Equipment

Driven mass–spring (unknown m, k, b)
Variable-frequency drive
Amplitude meter

Experiment

Driven mass–spring. Live amplitude A. Bench parameters are not labelled.

Oscillator parameters are hidden. You only change the drive angular frequency ω. Watch the live amplitude and record the ω where A is largest. The bench does not mark the peak.

Angular frequency ωω = 3.00 rad/s

Amplitude A = 0.094 m

The row stores only ω. Repeat the hunt at least 6 times (you may start from different ω). Processing uses the mean of the ω column.

Measurements

№	ω rad/s
No measurements yet — take your first reading.

Data processing

Add at least 2 trials to compute the sample mean.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Forced Oscillator: Natural Frequency from the Resonance Peak

Generated: 24 Aug 2026, 22:30

Goal

Determine ω₀ as the drive frequency of maximum steady amplitude. Light damping makes ω_res ≈ ω₀.

Measurement table

#	ω (rad/s)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 trials to compute the sample mean.

Conclusion

The mean drive frequency at peak amplitude agrees with ω₀. Main uncertainties: discrete ω steps and judging the peak by eye. Light damping keeps ω_res very close to ω₀.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

Steady amplitude A(ω) = (F₀/m) / √((ω₀²−ω²)² + (bω/m)²) peaks at ω_res = ω₀√(1−2ζ²). For small ζ, ω_res ≈ ω₀. The bench hides m, k, b, ω₀, ζ and any theoretical A(ω) curve. A live amplitude meter is the instrument — there is no resonance marker.

Procedure

The oscillator parameters are hidden. You only change the drive angular frequency ω.
Watch the live amplitude. Park at the peak. The bench does not mark ω₀.
Record that ω. Repeat the hunt at least 6 times (you may start from different ω).
Take the mean of the ω column and compare with the reference.

Conclusion

The mean drive frequency at peak amplitude agrees with ω₀. Main uncertainties: discrete ω steps and judging the peak by eye. Light damping keeps ω_res very close to ω₀.