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The critical damping coefficient of a single-degree-of-freedom system equals

  • A.\( 2\sqrt{km} \)
  • B.\( \sqrt{km} \) without the factor of two
  • C.\( km \) with no square root taken at all
  • D.\( 2\sqrt{k/m} \) with the ratio in place of the product

Answer: A

Equivalently \( c_c = 2m\omega_n \), and the damping ratio is \( \xi = c/c_c \). Expressing damping as this ratio makes the figure comparable across structures of any size. Both forms follow from setting the discriminant of the characteristic equation to zero.

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