Damped Oscillator Calculator
Damping ratio, regime (under/critical/over-damped), damped frequency, Q factor and decay time.
How to use the Damped Oscillator Calculator
- Enter or select: Mass m, Damping coefficient b, Spring constant k.
- The results (Natural frequency ω₀, Damping ratio ζ, Regime, Damped frequency ω_d, Quality factor Q, Amplitude decay time 2m/b, Logarithmic decrement) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- m x″ + b x′ + k x = 0
- ζ = b / (2√(mk))
- ω_d = ω₀√(1 − ζ²)
- Q = 1/(2ζ)