Right, I'm about to open a big can of worms:(adsbygoogle = window.adsbygoogle || []).push({});

I'm investigating eddy current damping of Simple Harmonic motion and I'm going to be investigating how the damping coefficient varies with various factors including the distance of the magnetic field (irrelevant, just informing). A "magnetic tunnel" creates eddy currents which damp the metallic glider on an air track. I hope the setup is clear.

However, since I am using a glider on an air track and a motion sensor, I've to attach a target on the glider which the motion sensor tracks (to record the simple harmonic motion). The problem is that this target is of such a shape that it'll offer plenty of air resistance (it's a flat rectangular sheet, perpendicular to the plane of motion). So the problem is that air resistance will no longer be negligible, but has to be reasonably taken into account. Hence attempting to find the damping coefficienet with air resistance being offered, will give an incorrect value (since I am purely interested in the value of the damping coefficient due to eddy current damping from the magnetic field).

So, my proposal is, say I found the damping coefficient with just air resistance (no magnetic tunnel), and then with the magnetic field AND air resistance, how would I get the damping coefficient due to the magnetic field ONLY?

i.e. if I wanted the damping coefficient due to eddy currents (magnetic field) ONLY, would I SUBTRACT the damping coefficient of AIR from damping coefficient of (air + eddy currents)?? (i.e. to get an accurate value, so as to remove the effect of air resistance damping from the value). Basically, are there any known theories/mathematics for "combined damping"?

Secondly, this is slightly beyond my physics course but since I have done differential eqns e.t.c I'm fairly comfortable with the mathematics involved. I will be mainly investigating an underdamped system, and so will be sketching a graph of log (maximum displacements from the SHM sinusoidal curve) against time and getting the gradient to find the value of the damping coefficient. However I believe it's not SOLELY the value of the gradient which gives the damping coefficient - apparently you have you equate it to something? The problem is this is slightly beyond my course however seems doable. Could someone please advise on how to get the damping coefficient from the gradient, as there various different D.E s describing the motion and research is only further confusing.

edit: Could you confirm that this would be the equation for underdamped motion:

https://www.physicsforums.com/latex_images/44/444951-1.png [Broken]

And hence plotting ln(x) against t would yield a slope equal to -b/2m? (and then obviously just proceed to solve for b)

I hope someone can help. There is practically nothing on this (multiple damping coefficients) on the internet!!! Feedback/help much appreciated.

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# Homework Help: SHM MULTIPLE damping coefficents practical help!

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