Resonance
The phenomenon in which a system oscillates with maximum amplitude when driven at its natural frequency. At resonance, the driving force is in phase with velocity, ensuring maximum energy transfer. Resonance peaks are sharp for lightly damped systems and broad for heavily damped ones. Resonance is crucial in applications ranging from musical instruments to electronic circuits.
Formula
f_resonance = f₀ = (1/2π)√(k/m)
Real World
Opera singer Ella Taylor can shatter a wine glass by singing a sustained note at its natural resonant frequency — the glass vibrates with increasing amplitude until it breaks.
Exam Focus
Sketch resonance curves for different damping levels; examiners award marks for correctly showing peak height and width changing with damping.
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