Damped Harmonic Oscillator Calculator
Compute damping ratio, natural/damped frequency and Q of a damped oscillator.
Input Data
Mass m.
kg
Spring constant k.
N/m
Damping c.
N·s/m
Results
ζ = c/(2√(mk)).
0.1
ω₀ = √(k/m).
10rad/s
ω_d = ω₀√(1−ζ²).
9.949874rad/s
Q = 1/(2ζ).
5
2√(mk).
20N·s/m
At a glance:ζ = c/(2√(mk)); ω₀ = √(k/m); ω_d = ω₀√(1−ζ²). Complements damped-oscillation and critical-damping.
Formula
ω₀ = √(k/m).
ζ = c/(2√(mk)).
$$\omega' = \sqrt{\omega_0^2 - \gamma^2}$$$$Q = \frac{\omega_0}{2\gamma}$$How to Use
- Enter m, k and c.
- The tool returns ζ, frequencies and Q.
Case Studies
m=1, k=4, c=0.5
ζ=0.125, ω₀=2, Q=4.
FAQ
ζ > 1?
Overdamped — no oscillation; ζ<1 underdamped (oscillates).
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.