Question

A damped vibrating system starting from rest has a initial amplitude of 20cm which reduces to 2 cm after 100 complete oscillation each of period 2.303 scond .Find the logarithmic decrement of system?

Answer 1

A damped vibrating system starting from rest has a initial amplitude of 20cm which reduces to 2 cm after 100 complete oscillation each of period 2.303 scond. Find the logarithmic decrement of system? 0.023

**Solution:**

N = 100 – the number of oscillations;

T = 2.303s – period of the oscillations;

A₁ = x(t) = 0.2m – initial amplitude;

A₁₀₀ = x(t + N · T) = 0.02m – amplitude after time N · T;

Formula for the logarithmic decrement of the system:

$$\delta = \frac{1}{N} \ln \left(\frac{x(t)}{x(t + N \cdot T)}\right) = \frac{1}{100} \ln \left(\frac{0.2m}{0.02m}\right) = 0.023$$

Answer: logarithmic decrement of the system is δ = 0.023