Waves
Resonance Amplitude
Maximum amplitude occurs when driving frequency equals natural frequency (resonance).
Variables
Amaxm
Maximum amplitude
Peak response amplitude
ωrad/s
Driving frequency
Applied frequency
ω₀rad/s
Natural frequency
Resonant frequency
Derivation
For driven oscillator, amplitude A = F₀/√((k-mω²)² + b²ω²) is maximum near ω = ω₀ = √(k/m).
Your notes
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Where this formula is listed
- Waves formulas, under Simple Harmonic Motion, alongside SHM Displacement, SHM Velocity, SHM Acceleration, SHM Maximum Velocity and Pendulum Period.
- In the waves list it comes after Quality Factor (Q Factor) and before Wave Equation.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Resonance Amplitude formula?
Resonance Amplitude is written A_max at ω = ω₀. Maximum amplitude occurs when driving frequency equals natural frequency (resonance). It belongs to Waves, under Simple Harmonic Motion.
What are the units in A_max at ω = ω₀?
In SI units, A_m ax is maximum amplitude, measured in m; ω is driving frequency, measured in rad/s; ω₀ is natural frequency, measured in rad/s.
How is the Resonance Amplitude formula derived?
For driven oscillator, amplitude A = F₀/√((k-mω²)² + b²ω²) is maximum near ω = ω₀ = √(k/m). The result is A_max at ω = ω₀.