Discussion
A structure has a mass of 10,000 kg and a stiffness of 4,000 kN/m. Its critical damping coefficient is nearest to
Answer: D
Correct answer: 400 kN·s/m
Critical damping is
\[ c_{cr} = 2\sqrt{km} = 2\sqrt{4 \times 10^{6} \times 10^{4}} \]
\[ = 2\sqrt{4 \times 10^{10}} = 2 \times 2 \times 10^{5} = 4 \times 10^{5}\ \mathrm{N\,s/m} = 400\ \mathrm{kN\,s/m} \]
Keeping the units consistent is the whole difficulty: stiffness must be in newtons per metre before the root is taken. Critical damping is the value at which free motion returns to rest without oscillating, and it is the reference against which real damping is expressed.
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