Discussion
Inertia force on a vibrating mass acts
Answer: A
Correct answer: opposite to the direction of its acceleration
The inertia force is \( -m\ddot{u} \), so it opposes the acceleration - the mass's resistance to being accelerated, written as though it were a force.
That sign is what makes D'Alembert's principle work: adding the inertia force to the real forces produces a set that sums to zero, so the dynamic problem can be handled with the methods of statics. Its direction has nothing to do with gravity, which enters separately as a static load.
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