GATE AG 2010 • Q32 MCQ • 1 Mark

Section 2: Farm Machinery

Machine Design

Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts

Question Statement:

The tractor seat vibrates with a frequency of 1 Hz when there is no damping. When damping is provided, the frequency of damped vibration is reduced by 10%. The damping factor is

Options:

  • (A) 0.21
  • (B) 0.39
  • (C) 0.44
  • (D) 0.93

Official Answer Key:

C

Step-by-Step Solution & Explanation

ωd = ωn√(1−ζ²). Given ωd = 0.90 ωn: 0.81 = 1 − ζ² ⇒ ζ² = 0.19 ⇒ ζ = 0.436 ≈ 0.44.

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