Discussion
A single-degree system has a period of 0.5 s. If a mass equal to the original is added, the new period is nearest to
Answer: D
Correct answer: 0.71 s
Period varies with the square root of mass:
\[ T = 2\pi\sqrt{\frac{m}{k}} \qquad \frac{T_2}{T_1} = \sqrt{\frac{2m}{m}} = \sqrt{2} \]
\[ T_2 = 0.5 \times 1.414 = 0.71\ \mathrm{s} \]
The distractor 1.00 s doubles the period, treating the relation as linear. The square root also explains why adding mass is an inefficient way of lengthening a period: doubling the mass buys only 41 per cent more period, and attracts more seismic force in proportion to the mass added.
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