Discussion
True or false: increasing the damping of a structure shortens its natural period appreciably.
Answer: C
Correct answer: False, because the damped and undamped frequencies differ negligibly at practical damping levels
The relation is \( \omega_d = \omega_n\sqrt{1-\xi^2} \), and at 5 per cent damping the factor is 0.99875 - a difference of about an eighth of one per cent in the period.
So damping does lower the frequency, but by an amount no measurement would resolve, which is why codes use the undamped period throughout. The second option overstates the case in the other direction: damping has a large effect on the amplitude of response, particularly near resonance, and only a negligible one on the period.
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