Discussion
For light damping the logarithmic decrement is approximately
Answer: C
Correct answer: \( 2\pi\xi \)
The exact relation is
\[ \delta = \frac{2\pi\xi}{\sqrt{1-\xi^2}} \]
and for light damping the square root is close to one, leaving \( \delta \approx 2\pi\xi \).
The approximation is excellent at practical levels: at 5 per cent damping the error is about a tenth of one per cent. Inverting it gives the working formula \( \xi \approx \delta/2\pi \), which is how a decay record is turned into a damping ratio.
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