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Driven Harmonic Oscillator Resonance Amplitude Calculator

A_ss = (F₀/m) / √((ω₀²−ω²)² + (2γω)²).

Compute the steady-state amplitude of a driven, damped harmonic oscillator with driving force F₀cos(ωt) and damping γ = b/(2m). A_ss = (F₀/m) / √((ω₀²−ω²)² + (2γω)²). Amplitude peaks at ω ≈ ω₀ for low damping. Reports A_ss and the peak (resonant) amplitude A_peak ≈ F₀/(2mγω₀) (low-damping limit).

Nadia Almasri By Nadia Almasri
Published Last reviewed 1 min read

Inputs

N
kg
rad/s
rad/s
s⁻¹

Results

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

A = (F₀/m) / √((ω₀²−ω²)² + (2γω)²).

In depth

Compute the steady-state amplitude of a driven, damped harmonic oscillator with driving force F₀cos(ωt) and damping γ = b/(2m). A_ss = (F₀/m) / √((ω₀²−ω²)² + (2γω)²). Amplitude peaks at ω ≈ ω₀ for low damping. Reports A_ss and the peak (resonant) amplitude A_peak ≈ F₀/(2mγω₀) (low-damping limit).