Discussion
Doubling the mass of a single-degree-of-freedom system multiplies its natural period by
Answer: C
Correct answer: 1.41
\[ T \propto \sqrt{m} \quad\Rightarrow\quad \frac{T_2}{T_1} = \sqrt{2} = 1.41. \] Doubling the mass therefore lengthens the period by about 41 per cent, not by a factor of two. It also increases the seismic weight, so the force demand may rise even though the longer period moves the structure to a lower point on the spectrum.
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