# Very difficult problem

1. Nov 20, 2006

### dukeh

You have a metal string and a magnetic field in the same direction of the rope-s axis.
The rope has two fixed extremes.
Find the general solution of the oscillations(transverse and longitudinal).
Data:
density of mass
linear density of charge P
arbitrary initial conditions
magnetic induction B
Use every data you want, the impotant thing is the solution of the problem
I think PDE are necesary to solve this problem

Last edited: Nov 21, 2006
2. Nov 21, 2006

### Staff: Mentor

Welcome to PF, dukeh. You must show your work in order for us to help you. What do you know about oscillations on a rope with fixed ends? And what in the world does a magnetic field have to do with a non-conducting rope?

3. Nov 21, 2006

### dukeh

Its not a rope, its a metal string. Thanks for the observation.

4. Nov 21, 2006

### dukeh

I know the string equations from the book Tikhonov Samarski about PDE, but those aparently are not enough

5. Nov 21, 2006

### OlderDan

I think you are expected to assume the linear charge density is constant along the length of the string. At least it should be assumed to start out that way. If you were to pluck the string and set up a standing wave the charges in motion would interact with the magnetic field. What effect would this have on the string? What do you think the steady state solution would be?

6. Nov 22, 2006

### dukeh

the linear density of charche is constant, its not a distribution
the density of mass is also constant
The physical interpretation is one of the problems I have had, I would really appreciate any colaboration with the problem.

7. Nov 22, 2006

### OlderDan

What happens to a charged particle that is moving perpendicular to a magnetic field?

8. Nov 23, 2006

### dukeh

9. Nov 23, 2006

### Staff: Mentor

10. Nov 26, 2006

### OlderDan

You can use this derivation as a guide

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/waveq.html#c3

There will be an addional force term related to the motion of charges in the magnetic field. Instead of looking for a solution where y is a function of x and t, look for a solution to r(x) independent of time where the acceleration from all the forces acting on a mass dm is a centripetal acceleration. r(x) is the displacement of the string from equilibrium at point x.

11. Nov 27, 2006

### OlderDan

A solution exists with the string in a rotational mode, which happens to be a valid solution whether the magnetic field is present or not. Try grabbing the end of a rope held firmly at the opposite end and see if you can set up a standing rotational wave by moving your hand in a circle.

The full solution to any string plucking problem is rather complex. If you have to work out the solution including all the transient motion, then you still have to recognize that the velocity dependent force from the magnetic field is going to drive the string out of plane and it will eventually work its way into the rotational mode.

Last edited: Nov 27, 2006
12. Nov 27, 2006

### HalfManHalfAmazing

dukeh, stop wasting everyone's time. i'm not sure how you got to where you are with that HORRIBLE spelling. "You dont know nothing about Fhysics"

Hahaha. Go back to grade 10.

13. Nov 27, 2006

### OlderDan

Why don't you just post your solution to the problem?

14. Nov 27, 2006

### Staff: Mentor

bye bye

That will be enough of that.

15. Nov 27, 2006

### Staff: Mentor

I just looked up the definition of "patience" in my dictionary, and Dan's picture was there.

I'm locking this thread for now. Maybe we should just delete the dang thing.