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Mechanical Engineering QUESTION #2435
Question 1
The undamped natural circular frequency \(\omega_n\) of a spring-mass system (mass \(m\), spring stiffness \(k\)) is:
  • \(\omega_n = \sqrt{k/m}\)✔️
  • \(\omega_n = \sqrt{m/k}\)
  • \(\omega_n = k/m\)
  • \(\omega_n = 2\pi\sqrt{m/k}\)
Correct Answer Explanation
From the equation of motion \(m\ddot{x}+kx=0\), dividing by \(m\) gives \(\ddot{x}+\omega_n^2 x=0\) where \(\omega_n^2=k/m\), hence \(\omega_n=\sqrt{k/m}\) rad/s.