Resonance in Forced Oscillations
When a sinusoidal driving force's frequency approaches the system's natural frequency sqrt(k/m), the steady-state amplitude grows sharply; with zero damping at exact resonance the particular solution gains a factor of t and grows without bound. Damping caps the peak amplitude at 1/(c*omega) scale and shifts the peak slightly below the natural frequency.
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When a sinusoidal driving force's frequency approaches the system's natural frequency sqrt(k/m), the steady-state amplitude grows sharply; with zero damping at exact resonance the particular solution gains a factor of t and grows without bound. Damping caps the peak amplitude at 1/(c*omega) scale and shifts the peak slightly below the natural frequency.
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