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.**