Discussion
For a structure subjected to base motion \( \ddot{u}_g \), the effective forcing on the equation written in relative coordinates is
Answer: C
Correct answer: \( -m\ddot{u}_g \)
Writing the equation in coordinates relative to the moving base gives
\[ m\ddot{u} + c\dot{u} + ku = -m\ddot{u}_g \]
so the ground acceleration appears as an equivalent force proportional to the mass. That is why base excitation and applied loading can be handled by the same machinery, and why seismic demand scales with mass - a heavier building attracts a larger effective force from the same ground motion. The negative sign follows from the change of reference frame.
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