I wonder, why in a linear DC machine
I wonder why these have exponential behavior

http://www.pasteall.org/pic/show.php?id=9327

a mathematical proof would be even an extra cool thing =]

 

I'm not able to interpret the second diagram properly. But I guess that thing has some capacitance or inductance to exhibit that exponential transient behaviour.
A look at the chapter rc and rl circuits of william hayt (Engineering circuit analysis) will clear your doubts regarding the exponential behaviour(it also has mathematical explanation). Here's a short explanation
http://www.allaboutcircuits.com/vol_1/chpt_16/2.html

 

nara: no, no inductance nor capacitance

it is a system like this

http://www.cramster.com/answers-dec...wire-mass-slides-friction-horizo_1081976.aspx

 

It has both Electric and magnetic field and the metal bar is in motion. That's tough. Only simple answer is that this has some sort of inductance/capacitance associated with it that causes that exponential behaviour(since it involves generator and magnetic field it should have it). Maybe someone else can answer it better

 

maybe first order response?

 

Check your understanding of "linear". It does not mean that the responses of the system are linear functions. Is that what you were expecting?

http://en.wikipedia.org/wiki/Linear_system

Differentiation is definitely a linear operator within the context of the above article. So is integration

 

thanks, reading here...

http://www.me.cmu.edu/ctms/modeling/firstorder/systemidentification/mainframes.htm

 

I'm not sure what the link is between the problem in post #3 and the fuzzy working in post #1.

The problem in post #3 probably has a simple solution.

Since the current is driven by a constant current source the force on the sliding conductor will be constant with the constant vertical B field. The velocity of the sliding bar would then increase in an unbounded manner in the absence of friction.

Force=B*d*i=m*a where a is the acceleration

v(t)=1/2*a*t^2