Discussion
For a model whose smallest natural period is 0.02 s, the central difference stability limit on the time step is nearest to
Answer: B
Correct answer: 0.0064 s
Apply the stability condition:
\[ \Delta t \le \frac{T_{min}}{\pi} = \frac{0.02}{3.1416} = 0.00637\ \mathrm{s} \]
Note that the shortest period governs, not the fundamental - so refining a mesh, which introduces ever higher modes, tightens the limit even though those modes contribute nothing to the response. That is the characteristic difficulty of explicit integration and the reason implicit schemes are preferred for structural earthquake analysis.
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