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GATE 2019 ME (ME2) – Question 42

Vibrations · Free vibration of single degree of freedom systems, damping · 2 marks · Multiple choice

The slender uniform rigid bar of mass m is hinged at O and supported by springs 3k and k and damper c as shown. Find $c/\sqrt{km}$ for critical damping.

Diagram for GATE 2019 ME (ME2) question 42
  1. 2
  2. 4
  3. $2\sqrt7$
  4. $4\sqrt7$

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Show answer and explanation

Correct answer: (D) $4\sqrt7$

Explanation

About the hinge, $I= mL^2/12+m(L/4)^2=7mL^2/48$. Rotational stiffness is $K_\theta=3k(L/4)^2+k(3L/4)^2=3kL^2/4$. Rotational damping is $C_\theta=c(L/4)^2$. Setting $C_\theta=2\sqrt{IK_\theta}$ gives **$c/\sqrt{km}=4\sqrt7$, D**.