Question

A damped vibrating system starting from rest has an initial amplitude of 20 cm which reduces to 2 cm after 100 complete oscillations each of period 2.3 second. Find the logarithmic decrement of the system.

Answer 1

Formula for the logarithmic decrement of the system:

$$\delta=\frac{1}{N}\ln{\frac{x(t)}{x(t+NT)}}\\\delta=\frac{1}{100}\ln{\frac{0.2}{0.02}}=0.023$$