// multi-utility computation suite · offline · instant · precise
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sci.damped-natural-frequency-SDOF Calculator
Calculates damped natural frequency ω_d = ω_n√(1−ζ²), amplitude decay, and phase from mass, stiffness, and damping ratio ζ. Critical damping (ζ = 1) prevents oscillation — most structures are lightly damped (ζ = 0.01–0.05) and ring for many cycles before decaying.
Inputs
Omega N Rad S
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Zeta
Reference formula or conversion factor shown for context.
K N M
Reference formula or conversion factor shown for context.
M Kg
Total mass (kg). Distinct from weight — weight = mass × gravity. Mass is constant; weight varies with location.
Results
damped natural freq ωd (rad/s)
The value at the specified point or condition.
damped freq fd (Hz)
Reference formula or conversion factor shown for context.
damped period Td (s)
Reference formula or conversion factor shown for context.