Re: [Phys-l] drop a metal cylinder through a solenoid

[John Denker <jsd@av8n.com>]

On 03/23/2012 10:39 AM, Carl Mungan wrote:
> 1. A cylindrical magnet is a pendulum bob on a toothpick arm swinging 
> entirely between two parallel Al plates. The two flat faces of the 
> magnet are its poles and they are parallel to the plates.
>
> 2. A cylindrical Al bob on the same arm swinging entirely within two 
> poles of a large C-shaped magnet. For simplicity, assume the pivot of 
> the toothpick is at the center of a pole face, so the bob always sees 
> the same strength magnetic field as it swings. That strength is the 
> same as that of the magnet bob in case 1. Size of bob and plates are 
> about the same in both cases.
>
> Which pendulum will have a shorter period and why? 

I am mystified by some details of the question:

A) The dominant effect of the magnetism will be eddy-current damping,
 yet the question asks about "period".  
  i) For small damping, the period of an oscillator is independent of 
   the damping.
  ii) For large damping, the system doesn't have a period.  It doesn't
   oscillate.  It's overdamped.

B) Assuming the question meant to ask about damping:  The two cases are 
 so dissimilar that I don't understand where the question is coming from.
 In case (1) there is a huge amount of eddy current damping, while in 
 case (2) there is almost none.

 Perhaps the question comes from a misunderstanding of Galileo's principle
 of relativity.  We agree that it doesn't matter which thing is moving ...
 but it matters a great deal whether the magnetic field is spatially
 nonuniform (case 1) or uniform (case 2).

> In fact if it wasn't for the fact 
> that the bob's velocity is variable ......

In case (2), the variation in velocity will lead to "some" electromagnetic
damping, but it will be small compared to case (1) and small compared to
ordinary nuisance damping (air friction, pivot friction, et cetera).