Discussion
In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m.
The logarithmic decrement of the vibrating system is
Answer: A
The logarithmic decrement is about 0.63.
The damping ratio is \(\zeta = c/c_{c} = 35/350 = 0.1\). Then
\[ \begin{aligned} \delta &= \frac{2\pi\zeta}{\sqrt{1 - \zeta^{2}}} \\ &= \frac{0.6283}{0.995} = 0.631 \end{aligned} \]
For light damping \(\delta \approx 2\pi\zeta = 0.628\) anyway. 1.26 and 1.89 are two and three times the correct value, and 0.32 is half of it, as if \(\pi\zeta\) were used.
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