The GATE Grind

GATE 2026 ME – Question 18

Vibrations · Free vibration of single degree of freedom systems, damping · 1 mark · Multiple choice

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m. The logarithmic decrement of the vibrating system is

  1. 0.63
  2. 1.26
  3. 0.32
  4. 1.89

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Correct answer: (A) 0.63

Explanation

The damping ratio is $\zeta = \frac{35}{350} = 0.1$. The logarithmic decrement is $\delta = \frac{2\pi\zeta}{\sqrt{1 - \zeta^2}} = \frac{0.6283}{0.995} = 0.63$.