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Mechanical Engineering QUESTION #2438
Question 1
For an underdamped system (\(\zeta < 1\)), the damped natural frequency \(\omega_d\) (quasi-circular frequency \(b\)) is:
  • \(\omega_d = \omega_n / \sqrt{1-\zeta^2}\)
  • \(\omega_d = \omega_n\sqrt{1-\zeta^2}\)✔️
  • \(\omega_d = \omega_n(1-\zeta)\)
  • \(\omega_d = \omega_n + \zeta\)
Correct Answer Explanation
For the underdamped case, the damped natural frequency is \(\omega_d=\omega_n\sqrt{1-\zeta^2}\). Since \(\zeta<1\), \(\omega_d<\omega_n\).