Discussion
The dynamic magnification factor at resonance for a lightly damped system is approximately
Answer: D
Correct answer: \( 1/2\xi \)
At resonance the exact magnification is \( 1/(2\xi\sqrt{1-\xi^2}) \), which for light damping reduces to \( 1/2\xi \).
The relation shows how completely damping governs the resonant response: at 5 per cent the amplification is 10, at 2 per cent it is 25, and as \( \xi \to 0 \) it grows without bound. Away from resonance damping matters far less, which is why an accurate damping estimate is needed only where the forcing is close to a natural frequency.
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