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i have uploaded my question. please check out the attached .pdf file.
Homework Equations
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I think it's just a sloppy and misleading way to describe the direction. Note how they 'derive' the inertia force: It's just the negative of 'ma'.it has been mentioned in this website that 'inertia force acts opposite to the direction of motion'.
did i understand it right?
as i defined downward x as positive, so does that mean x¨ is positive as i move downwards away from equilibrium?Since your variable x already defines the positive direction of acceleration, x¨, the inertia force is simply −mx¨
[itex]\ddot{x}[/itex] is positive as long as the acceleration is in the positive direction, which you have defined as downward. Note that the restoring force of the spring always acts to accelerate the mass back towards the equilibrium point. So at any point below the equilibrium point, the acceleration would be upward.as i defined downward x as positive, so does that mean x¨ is positive as i move downwards away from equilibrium?
You wouldn't put the acceleration on a free body diagram, but it would act upward.i might be asking really very silly doubt but this thing is really confusing me. i want it to be sorted.
as the mass moves away from equilibrium towards +A in the downward positive x direction, if we draw a free body diagram, how do we represent acceleration?
[itex]\ddot{x}[/itex] would be negative and the inertia force would be positive. But you don't have to worry about the inertia force directionyou'd still represent that inertia force as [itex]m\ddot{x}[/itex].if we take x¨, acceleration positive in the downward direction, the inertia force acts in the opposite direction i.e, upwards.
Right.so if i write equation of motion using D'Alembert's Principle, i get:
mx¨  kx = 0.
So now you are looking at the situation when the mass is above the equilibrium point. So the spring force acts downward and the acceleration is downward.but if i consider the situation where the mass is at a position, away from A, towards equilibrium, then what is the direction of acceleration and how do i write the equation of motion?