Discussion
The logarithmic decrement of a decaying free vibration is defined as the natural logarithm of the ratio of
Answer: B
Correct answer: two successive peak amplitudes
The logarithmic decrement is
\[ \delta = \ln\frac{u_i}{u_{i+1}} \]
taken from a free vibration record. The ratio is constant from cycle to cycle for viscous damping, which is what makes a single measurement meaningful and lets several cycles be averaged for accuracy.
It is the simplest experimental route to the damping ratio: displace the structure, release it, and measure the decay. No forcing equipment is needed, unlike the half-power bandwidth method.
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