Can PDE Solve the Oscillations of a Metal String in a Magnetic Field?

[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

 

[berkeman]

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?

 

[dukeh]

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

 

[dukeh]

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

 

[OlderDan]

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

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?

 

[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.

 

[OlderDan]

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.

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

 

[dukeh]

Please help!

 

[berkeman]

Show your work.

 

[OlderDan]

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

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.

 

[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.

 

[HalfManHalfAmazing]

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

Hahaha. Go back to grade 10.

 

[OlderDan]

Older Dan you are a ****ing piece of chet
You don't know nothing about Fhysics

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

 

[Doc Al]

bye bye

That will be enough of that.

 

[berkeman]

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

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.