Damped Oscillation Calculator
Compute damped frequency, half-life and Q of a decaying oscillation.
Input Data
Natural Frequency Hz
Hz
Damping Coeff Per S
1/s
Results
f_d = √(f₀² − (β/2π)²).
0.999873Hz
Time for amplitude to halve.
6.931472s
Q = π·f₀/β.
31.415927
Under/over/critical.
0
At a glance:f_d = √(f₀² − (β/2π)²); Q = πf₀/β. Complements damped-harmonic-oscillator and decay.
Formula
f_d = √(f₀² − (β/2π)²).
$$\omega_d = \sqrt{\omega_0^2 - \gamma^2}, \quad A(t) = A_0 e^{-\gamma t}, \quad Q = \frac{\omega_0}{2\gamma}, \quad t_{1/2} = \frac{\ln 2}{\gamma}$$How to Use
- Enter natural frequency and damping.
- The tool returns damped frequency, half-life and Q.
Case Studies
f₀=1, β=0.1
f_d≈0.998, Q≈31.4.
FAQ
Half-life of amplitude?
t½ = ln2/β.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.