Spring-Mass-Damper Natural Frequency & Damping Calculator
Calculate undamped and damped natural frequency (fn, fd), critical damping (cc), damping ratio (zeta), and logarithmic decrement for single-degree-of-freedom mechanical systems.
System Mass, Stiffness & Damping
kg
N/m
20,000 N/m = 20.0 N/mm
N·s/m
Set c = 0 for ideal undamped oscillation
Natural Frequency (fn)
UNDERDAMPED (ζ = 0.075)
3.18 Hz
Angular frequency (ωn): 20.00 rad/s | Period: 0.314 s
Damped Frequency (fd)
3.17 Hz
ωd = 19.94 rad/s (99.7% of ωn)
Critical Damping (cc)
2,000 N·s/m
Damping ratio: ζ = 0.075 (7.5%)
Decay & Static Deflection
Logarithmic Decrement (δ):
0.473
Amplitude Decay per Cycle:
62.3% remaining (-37.7%/cycle)
Static Gravity Deflection (δst):
24.5 mm (under 1g load)