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Mechanical Engineering QUESTION #2436
Question 1
The critical damping coefficient \(c_{cr}\) for a spring-mass-damper system is:
  • \(c_{cr} = \sqrt{km}\)
  • \(c_{cr} = 2m\omega_n = 2\sqrt{km}\)✔️
  • \(c_{cr} = k/\omega_n\)
  • \(c_{cr} = m\omega_n^2\)
Correct Answer Explanation
Critical damping: \(\alpha=\omega_n\) where \(\alpha=c/(2m)\). Hence \(c_{cr}=2m\omega_n=2m\sqrt{k/m}=2\sqrt{km}\).