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Resonance & Damping Lab
Forced oscillations, resonance curves and damping · H2 Physics 9749 · Oscillations
driver / supportspring–massequilibrium ticksdrag to orbit · scroll to zoom · graphs show true values
Controls
Try first: slide fd to 1.00 × f₀ — watch amplitude explode.
natural frequency f₀ = √(k/m)/2π = 0.796 Hz
damping b1.50 N s/m
ⓘ more
Manual: set fd, wait for the steady-state badge — the point plots itself. Changing m or k clears the plot (different system). Damping changes start a new colour.
Response curve — steady-state amplitude vs driving frequency
Dashed line = f₀ · ring = current point (amber settling, green steady).
Readouts
f₀ natural
0.796 Hz
f_d driving
0.477 Hz
0.60 × f₀
amplitude
0.0 cm
settling…
phase lag φ
—
settling…
drivermass
φ ≈ 0 below f₀ · π/2 at resonance · → π above.
What to notice
Forced oscillations & resonance
- Once transients die away, the forced system oscillates at the driving frequency fd — not its natural frequency f₀. Watch the mass lock onto the driver.
- Resonance: when fd = f₀, the driver transfers energy to the system at the maximum rate → maximum amplitude.
- More damping → resonance peak lower and broader, with the peak shifted slightly below f₀ — build the curve family and see it.
- Resonance amplitude is large but finite: it grows until energy dissipated per cycle equals energy supplied per cycle.
Where you meet it
- Microwave oven: ~2.45 GHz microwaves drive water molecules near their natural frequency → maximum energy transfer heats the food.
- Radio tuning:the tuning circuit's natural frequency is adjusted to match one station's frequency — only that signal resonates and is picked out.
- Bridges:soldiers break step so their marching frequency never matches the bridge's natural frequency; engineers add damping (e.g. the Millennium Bridge fix).
- Car suspension: dampers close to critical damping stop the car bouncing after a bump.