Discussion
The equation of motion is written about the static equilibrium position so that
Answer: C
Correct answer: the self weight and its initial deflection drop out of the equation
Measuring displacement from the position the structure already occupies under its own weight makes the weight and the corresponding spring force cancel exactly, since they balance in that position.
What remains is the equation in terms of the dynamic displacement alone, and the response computed is the movement about the static position - which is what matters for stresses caused by the vibration. Damping, stiffness and mass all remain in the equation unchanged.
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