# Harmonic oscillations of the electromechanical system (normal modes)

1. Oct 24, 2014

### sergiokapone

1. The problem statement, all variables and given/known data
http://imagizer.imageshack.us/v2/275x215q90/661/kIVMcC.png [Broken]
Mathematical pendulum is the part of the oscillating circuit.
The system is in a constant uniform magnetic field. Oscillations is small. Find the normal modes of oscilations.

2. Relevant equations

$\begin{cases} ml^2\ddot \phi+ mgl\sin\phi=1/2\dot q Bl^2 \\ \frac{q}{C}+L\ddot q = 1/2Bl^2\dot \phi \end{cases}$
+
$\sin\phi \approx \phi$

3. The attempt at a solution

Submit a solution in the form $q=q_0e^{i\omega t}$ and $\phi=\phi_0e^{i\omega t}$.
It is more clear to me how to find for a solution. But I'm not sure for a signs near right sides of equations, e. g. near the $1/2\dot q Bl^2$ and $1/2 Bl^2\dot \phi$. How I can determine right signs.

I get right sides in first equation as mean Ampere force: $F=1/2IlB=1/2\dot q l B$,
and in second equation as EMF: $\epsilon=-B\frac{dS}{dt}$, where $dS=1/2lv$, $v=-l\dot \phi$. Thus, $\epsilon=\frac{Bl^2}{2}\dot\phi$

Another words, how can I determine right signs for the Ampere force and EMF?

Last edited by a moderator: May 7, 2017
2. Oct 29, 2014

### Greg Bernhardt

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Oct 29, 2014

### Dr.D

You have not indicated the direction you are taking for positive current; seems to me like this is a first step.

4. Oct 30, 2014

### sergiokapone

Ok, let it be clockwise.