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Doubling the stiffness of a single-degree system while holding its mass constant changes the natural frequency by a factor of

  • A.4
  • B.1
  • C.\( \sqrt{2} \)
  • D.2

Answer: C

Since \( \omega_n = \sqrt{k/m} \), the frequency follows the square root of stiffness, so it rises by about forty-one per cent. The period falls by the same factor. Halving the mass would have exactly the same effect on the frequency as doubling the stiffness.

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