Discussion
If the mass of a structure is quadrupled and its stiffness left unchanged, the natural period becomes
Answer: B
Correct answer: twice the original value
\[ T \propto \sqrt{m} \quad\Rightarrow\quad \frac{T_2}{T_1} = \sqrt{4} = 2. \] Quadrupling the mass doubles the period. Note that the quadrupled mass also quadruples the seismic weight, so unless the longer period moves the structure far enough down the spectrum, the base shear rises substantially.
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