Natural frequency and damping calculator
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Result
Natural frequency3.183 Hz
Angular natural frequency20 rad/s
Damping ratio0.1
Damped frequency3.167 Hz
Step-by-step solution
Undamped
ωn = √(k/m) = 20 rad/s
fn = ωn/2π = 3.183 Hz
Damping
ζ = c/(2√(km)) = 0.1 (underdamped)
Key formulas
- Natural frequency
- ωn = √(k/m), fn = ωn/(2π)
- From static deflection
- ωn = √(g/δst)
- Critical damping
- cc = 2√(km) = 2mωn
- Damping ratio
- ζ = c/cc
- Damped frequency
- ωd = ωn√(1 − ζ²)
- Logarithmic decrement
- δ = (1/n)·ln(x0/xn), ζ = δ/√(4π² + δ²)
- Springs in parallel
- k = k1 + k2
- Springs in series
- 1/k = 1/k1 + 1/k2
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