Discussion
From a logarithmic decrement of 0.288, the damping ratio is nearest to
Answer: A
Correct answer: 4.6 per cent
Invert the light-damping approximation:
\[ \xi \approx \frac{\delta}{2\pi} = \frac{0.288}{6.283} = 0.0458 = 4.6\% \]
The distractor 28.8 per cent takes the decrement itself for the ratio, forgetting the factor of \( 2\pi \). A result near 5 per cent is entirely typical of a concrete structure, which is a useful check - a decrement of 0.288 means successive peaks in the ratio \( e^{0.288} = 1.33 \), a visible but gentle decay.
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