Question

The logarithmic decrement of a pendulum is 0.3. Calculate the percentage change in successive amplitude.

Answer 1

25.9%

Answer 2

The logarithmic decrement $\delta$ is related to successive amplitudes $A_n$ and $A_{n+1}$ by $\delta = \ln(A_n/A_{n+1})$. Therefore, $A_{n+1}/A_n = e^{-\delta}$. The percentage change is given by $\frac{A_{n+1} - A_n}{A_n} \times 100\% = (A_{n+1}/A_n - 1) \times 100\%$. Substituting the value of $\delta = 0.3$: Percentage Change $= (e^{-0.3} - 1) \times 100\% \approx (0.7408 - 1) \times 100\% \approx -25.9\%$. The question likely refers to the percentage decrease, which is $(1 - e^{-\delta}) \times 100\% \approx 25.9\%$.