Problem: How to stick two formulas together

[Roadam]

Hi, I have been doing some theoretical work and I stumbled upon a problem that is way too tough for me at the present.

 

To explein the situation:

I have a coil of specific winding and know how does force upon feromagnetic material change with distance from coil center along its axis. That is when constant current is flowing trough it.

I did some integration and came to the equation of speed versus distance, that later gave me the average speed and the time in which material gets to the center of the coil. No problem yet.

 

The thing is that I want to know the speed vs distance equation if the current isnt constant. Lets say that the function of current versus time is sinusoidal, and that I only let trough the first half of oscilation. Or maybe even further, what must be the frequency of that oscilation be so that defined amount of magnetic material would reach the center of the coil when the current strikes zero.

[Qfwfq]

Looks like you're in for some tricky differential equations, that might not have an analytic solution for a given time dependence of the current.

[Roadam]

I figured out as much, maybe they are teaching some good tricks at university, which some of you have gone trough I suppose. I have not got there yet.

[sanctus]

Maybe try to post your equations, because electro was never my strength but if I see the equations maybe I (or someone else) come up with something...

[Roadam]

The fact is that I think that there is no problem with electro theory, its just equations, see them as two factors of force, one along distance and one along time. The problem is how to put them together trough Neutonian phsycs and make, lets say, equation of distance vs time.

[Qfwfq]

Well, up to here it isn't difficult, essentially:

 

[math]\Phi(x)\sin(\omega t + \phi) = m\frac{d^2x}{dt^2}[/math]

 

or some other function instead of the sine, but without specifying both those factors there's not much point in discussing how to integrate save for numerical methods.

[sanctus]

I don't think there is a general way of doing this "putting together" that's why I asked for the two equations...can't you just make a couple system of differential equations? Or maybe I didn't understand at all what you are looking for...

[Roadam]

 

[math]\Phi(x)\sin(\omega t + \phi) = m\frac{d^2x}{dt^2}[/math]

 

or some other function instead of the sine, but without specifying both those factors there's not much point in discussing how to integrate save for numerical methods.

 

Which two factors? X and t? Well lets say that x is predetermined and I am looking for specific t. As for both functions, the first is some third order polynomial which I cannot derive from equations but just from FEMM simulator(a program), the second one is sinusoidal, just as current varies in coil-condensator circuit.

 

If I understand this right, you just multiply functions together, but the other part is somewhat mysterious to me. I dont understand integrals and differentials so much(only last few months at high school). Lets say that I want to know the moment when combined equation is zero again, how must I integrate this. Anyway, I will try to put this into mathematica...

[Qfwfq]

Which two factors? X and t?

The functions of them, which I wrote as [imath]\Phi[/imath] and the sine, in the right hand side. The left hand side is just ma, with a being the second time derivative of x.

[Roadam]

Could you set me into direction of some site that deals with physical view of calculus? I`d better learn from ground up, than bother you with my strange problems. Becouse seriously, I dont have any good idea how to use your formula, even my tries in mathemathica havent brought any resoults.

 

As for differential equations... How could you set equations to get the travelling time if force varies with time itself and distance travelled, although final distance from the start is defined.

 

Or maybe someone knows for a physical sandbox program?