Discussion
A vibration record shows the amplitude halving every three cycles. The damping ratio is nearest to
Answer: A
Correct answer: 3.7 per cent
Halving over three cycles gives the decrement per cycle:
\[ \delta = \frac{1}{3}\ln 2 = \frac{0.6931}{3} = 0.2310 \]
\[ \xi \approx \frac{\delta}{2\pi} = \frac{0.2310}{6.283} = 0.037 = 3.7\% \]
Averaging over several cycles is standard practice, since it reduces the effect of noise on any single peak. The distractor 16.7 per cent takes the halving as a simple fraction spread over three cycles, ignoring both the logarithm and the \( 2\pi \).
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