Waves
Resonance Amplitude
Maximum amplitude occurs when driving frequency equals natural frequency (resonance).
Variables
A_maxm
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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Common questions
What is the Resonance Amplitude formula?
Resonance Amplitude is written Aₘₐₓ 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 Aₘₐₓ at ω= ω₀?
In SI units, A_max 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 Aₘₐₓ at ω= ω₀.