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GATE 2020 ME (ME2) – Question 17

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

The spring–mass–damper equation is $d^2x/dt^2+3\,dx/dt+9x=10\sin(5t)$. Find its damping factor.

  1. 0.25
  2. 0.5
  3. 2
  4. 3

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Show answer and explanation

Correct answer: (B) 0.5

Explanation

Compare with x″+2ζωn x′+ωn²x=forcing. Natural frequency is√9=3 and2ζ(3)=3, giving **ζ=0.5, B**. The forcing frequency5 does not set the damping ratio.