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Mechanical Engineering QUESTION #2437
Question 1
The damping ratio (critical damping ratio) \(\zeta\) for a viscously damped system is defined as:
  • \(\zeta = c\omega_n / k\)
  • \(\zeta = c / c_{cr} = c / (2m\omega_n)\)✔️
  • \(\zeta = c / (2k)\)
  • \(\zeta = \sqrt{c / (2mk)}\)
Correct Answer Explanation
The damping ratio \(\zeta = c/c_{cr} = c/(2m\omega_n) = c/(2\sqrt{km})\). Systems with \(\zeta<1\) are underdamped, \(\zeta=1\) critically damped, and \(\zeta>1\) overdamped.