Forced oscillations
Oscillations of a system driven by an external periodic force at a frequency f_drive. If the driving frequency matches the system's natural frequency f₀, resonance occurs, and amplitude increases dramatically. Damping limits resonant amplitude. Away from resonance, oscillation amplitude is determined by the driving force and the system's mechanical impedance.
Formula
A ∝ 1 / √((f₀² − f²)² + b²f²)
Real World
The Millennium Bridge in London wobbled violently on opening day in 2000 because crowds walking in step drove it at its natural frequency, causing resonant forced oscillations that forced its closure for two years.
Exam Focus
State that maximum amplitude occurs when driving frequency equals natural frequency, and explain damping's role in limiting it.
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