Really stuck

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I need to derive an equation of motion for how the ground resonates when a pneumatic drill is the driving force. The equation will use Newton's second law and I am totally stuck.
 
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So the system isn't a damped driven harmonic oscillator?
Being driven at [A (cos wt)] ? Because that's what it sounds like to me. :o
 
So the system isn't a damped driven harmonic oscillator?
Being driven at [A (cos wt)] ? Because that's what it sounds like to me. :o

I was thinking of reducing the system to a simple mass spring damper, to represent the drill but how do I incorporate the oscillations of the floor into this?
 
If your equation is for the ground, the drill will simply provide a driving force like daz says.

The ground will be damped with a co-ordinate dependent damping co-efficent that lets the ground vibrate less as the square of the distance from the drill.

You need to consider each annuli seperatley, with its own damping co-efficent and its own mass, with each annuli being driven by the one next ot it. if you wanted to be fancy you could incorperate phase into it as well.
 
If your equation is for the ground, the drill will simply provide a driving force like daz says.

The ground will be damped with a co-ordinate dependent damping co-efficent that lets the ground vibrate less as the square of the distance from the drill.

You need to consider each annuli seperatley, with its own damping co-efficent and its own mass, with each annuli being driven by the one next ot it. if you wanted to be fancy you could incorperate phase into it as well.

Yeh I see. I will represent the input force of the drill as a sinewave with a frequency equal to that of a pneumatic drill. I do not know what you mean by "annuli".
 
I am thinking the input will be an impulse function as the drill is only in contact with the ground for like 1/25 of a second.
 
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