(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello everyone. I'm trying to find the eiegenfrequencies in a problem.

We have a particle of mass m, charge e, that is subject to a linear restoring force

[tex]\textbf{F} = -k\textbf{r} [/tex]

and the particle is in a magnetic field [tex]\textbf{B} = B\textbf{k}[/itex]

(in the z-direction)

3. The attempt at a solution

I am a bit confused ecause I only get one eigen-frequency: sqrt(k/m), which is as though the magnetic field is not there.

In finding the freq.s you determine the kinetic and potential energy. Th magnetic field has no addittion to the potential energy? This is what I did. I took:

U = 0.5k(x^2 + y^2 + z^2)

T = 0.5mv^2

where v = <dx/dt, dy/dt, dz/dt>

which gave me the above answer, which I suspect is wrong, partly because the question goes on to say:

"Write your answer in terms of sqrt(k/m) and the cyclotron freq. Hint: use the variable u=x+iy"

I would be grateful for any help.

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# Homework Help: Finding eigenfrequencies

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