Structural Dynamics MCQ with answer and solution

Concept

Logarithmic decrement of damped structural system

Formula

δ = 2 × π × ζ

Step-by-step solution

1. Logarithmic decrement represents the rate at which the amplitude of a free damped vibration decreases. 2. The formula relating damping ratio ζ to logarithmic decrement δ is approximately δ = 2 × π × ζ. Answer: B

Explanation

For small damping ratios, the logarithmic decrement is given by the expression 2 × π × ζ, where ζ represents the damping ratio. Substituting ζ = 0.1 into the formula yields 2 × 3.14 × 0.1, which equals 0.628. Thus, option B is the correct answer.

Why the other options are wrong

C) 0.942 corresponds to three times π times the damping ratio rather than the correct formula output. D) 1.256 represents twice the standard logarithmic decrement value.

Shortcut

Logarithmic decrement δ = 2 × π × damping ratio = 2 × 3.14 × 0.1 = 0.628.

Common mistake

Incorrectly incorporating natural frequency into the logarithmic decrement formula instead of calculating δ as 2πζ.