Determine logarithmic decrement, if the amplitude of a vibrating body reduces to 1/6th in two cycles.

Question

Quizplus · Accepted Answer

The logarithmic decrement $\delta$ can be found using the formula $\delta = \frac{1}{n} \ln \frac{x_0}{x_n}$, where $x_0$ is the initial amplitude, $x_n$ is the amplitude after $n$ cycles, and $n$ is the number of cycles. Given that the amplitude reduces to 1/6th in two cycles, we have $x_0/x_n = 6$ and $n = 2$. Thus, $\delta = \frac{1}{2} \ln 6 \approx 0.8958$.

Determine Logarithmic Decrement, If the Amplitude of a Vibrating Body