Question

In a vibrating system, if the actual damping coefficient is 50 N/m/s and critical damping coefficient is 500 N/m/s, then logarithmic decrement is equal to:
1. 0.21
2. 0.45
3. 0.63
4. 0.87

Answer 1

Correct Answer - Option 3 : 0.63

Concept:

Logarithmic decrement (δ):

\(δ = \frac{{2\pi\xi }}{{\sqrt {1 -\xi ^{2}\;} }}\) and \(\xi = \frac{C}{{{C_c}}}\)

where C = Actual damping coefficient, C_c = Critical damping coefficient.

Calculation:

Given:

C = 50 N/m/s, C_c = 500 N/m/s

\(\xi = \frac{50}{{{500}}}\) = 0.1

\(δ = \frac{{2 \times \pi \times 0.1}}{{\sqrt {1 - {{\left( {0.1} \right)}^2}} }}\)

∴ δ = 0.63.