Damped Frequency Calculator
Enter the undamped natural frequency and damping ratio to instantly compute the damped natural frequency.
Inputs
Dimensionless. Use 0 < ζ < 1 for underdamped systems.
0 (no damping)
1 (critical)
1.5 (overdamped)
System Type
Results
Undamped natural frequency (ωn)
Damping ratio (ζ)
Damped frequency (ωd) — rad/s
Damped frequency (fd) — Hz
Damped period (Td)
Frequency reduction (ωd / ωn)
No oscillation
Formula
ωd = ωn × √(1 − ζ²)
Valid for 0 ≤ ζ < 1 (underdamped). For ζ ≥ 1 there is no oscillatory response.
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Summary
Enter the undamped natural frequency and damping ratio to instantly compute the damped natural frequency.
How it works
- Enter the undamped natural frequency (ωₙ) in Hz or rad/s.
- Enter the damping ratio (ζ) — a value between 0 and 1 for underdamped systems.
- The calculator applies the formula ωd = ωₙ × √(1 − ζ²).
- Results show the damped frequency in both rad/s and Hz.
- The damping classification (underdamped, critically damped, overdamped) is shown automatically.
Use cases
- Design mechanical vibration isolators and shock absorbers.
- Analyze structural dynamics of buildings, bridges, and machine frames.
- Tune suspension systems in automotive engineering.
- Determine resonant frequency shift in damped electrical LC circuits.
- Validate finite-element simulation outputs for dynamic systems.
- Estimate settling time in control system second-order responses.
Frequently Asked Questions
Last updated: 2026-06-10 ·
Reviewed by Nham Vu