Discussion
The central difference method for solving the equation of motion is
Answer: A
Correct answer: conditionally stable, with a limit on the time step
The central difference method is explicit, and explicit schemes are conditionally stable: the step must satisfy \( \Delta t \le T_{min}/\pi \), where \( T_{min} \) is the shortest period in the model.
The limit is set by the highest mode, which for a fine mesh may be of no interest whatever - so a model refined for accuracy forces very small steps. That is the trade against implicit methods such as Newmark's, which are unconditionally stable but require an equation solution at every step.
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