Discussion
Two structures have identical mass but one is twice as stiff. The stiffer one has
Answer: B
Correct answer: the shorter natural period
Period varies inversely with the square root of stiffness:
\[ T = 2\pi\sqrt{\frac{m}{k}} \qquad \frac{T_2}{T_1} = \frac{1}{\sqrt{2}} = 0.707 \]
so doubling the stiffness shortens the period by about 29 per cent. The square root matters: stiffening a structure is an inefficient way of changing its period, and on a typical design spectrum a shorter period often means a higher spectral acceleration, so the stiffer building may attract more force.
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