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GATE 2016 ME (ME2) – Question 20

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

A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is

  1. $q=\sqrt{2km}$
  2. $q=2\sqrt{km}$
  3. $q=\sqrt{2k/m}$
  4. $q=2\sqrt{k/m}$

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Correct answer: (B) $q=2\sqrt{km}$

Explanation

For mx-double-prime+qx-prime+kx=0, critical damping requires a repeated real root of the characteristic quadratic. Its discriminant vanishes: q²−4mk=0. Taking the positive coefficient gives **q=2sqrt(km), B**.