Scenario
Underdamped
ζ = 0.10 — decaying oscillation
Critically Damped
ζ = 1.00 — fastest return, no overshoot
Overdamped
ζ = 2.00 — sluggish exponential decay
Driven Resonance
ω = ω₀ — amplitude builds to max
Off-Resonance
ω ≠ ω₀ — transient beating
Natural freq ω₀
4.00
Damping γ
0.40
Drive amp F₀
0.00
Drive freq ω
4.00
Speed
1.0×
∼ Envelope
⏸ Pause
↺ Reset
x(t) above — phase portrait
(x, ẋ) below. Spiral = damped,
limit cycle = driven steady state.
ω₀:
4.00
γ:
0.40
ζ:
0.100
type:
Underdamped
t:
0.00
s
ỹ + 2γẋ + ω₀²x = F₀cos(ωt)
Presets
— switch damping regime
Sliders
— tune ω₀, γ, drive
Space
— pause ·
R
— reset