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The natural circular frequency of an undamped single-degree-of-freedom system is

  • A.\( \sqrt{m/k} \) with mass in the numerator instead
  • B.\( k/m \) without the square root being taken at all
  • C.\( 2\pi\sqrt{k/m} \) with an unnecessary factor included
  • D.\( \sqrt{k/m} \)

Answer: D

From \( \omega_n = \sqrt{k/m} \) the period follows as \( T = 2\pi/\omega_n \). Inverting the ratio inside the root is the most frequent slip, and it makes stiff systems appear slow. Doubling the mass therefore lengthens the period by about forty-one per cent.

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