Forced Damped Vibration Calculator
Calculate steady displacement amplitude, phase lag and force transmissibility of a viscously damped single-degree oscillator.
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Result
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Calculation steps
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How to calculate
Use harmonic steady-state response after transients have decayed, with force applied to the mass and a stationary support.
X=(F0/k)/√((1−r²)²+(2ζr)²); r=ω/ωn; ζ=c/(2√(km))
Worked example
At zero forcing frequency amplitude tends to the static deflection F0/k. At resonance r=1 with positive damping, amplitude is F0/(cωn).
Assumptions and input details
Linear mass/spring and viscous damping, force excitation rather than base excitation. Undamped exact resonance has no finite steady-state solution and is rejected. Transient initial conditions, nonlinear damping and physical travel/load limits are excluded.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
The 19 mass definitions distinguish avoirdupois and troy measures, metric and regional measures. Japanese kin is 600 g; mainland Chinese shijin is 500 g.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
SI prefixes are explicit: for example, milli means one thousandth, micro one millionth and kilo one thousand. Changing a unit changes the interpretation of the entered number.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
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Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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