# Magnetic Pendulum Experiment

Suppose we have a pendulum which is fixed at some point, P. We release it from some initial angle $$\theta$$ and it swings over a solenoid for which there exists some magnetic force. Note that there is a piece of string connecting from one end at a fixed point P, and the mass being swung is a small magnet at the other end.

If I wish to model this pendulum's motion, I believe that I cannot use the generic formula; $$y(t)=Ae^{-kt}cos(\omega t)$$ I believe that a more refined model may be required which includes the effect of such a magnetic field on the mass.

However, deriving this is seeming to be very difficult for me... Is there a possible way where we can include the effect of the magnetic field on the original mechanical system?

I have attempted to make an ODE in such a way that; $$y''+\alpha y'+\beta y=0$$ Where $$\alpha$$ and $$\beta$$ are just constants caused by friction.
After further thought I have attempted to make an ODE by considering the equation;

$$I(\omega^2)''=\tau_{gravity}+\tau_{Dampening}+\tau_{Magnetic}$$

Would this be on the right track? Or is there another path which I need to take?

• Have you established what the force between magnet and solenoid is? And what are the $\sigma$ representing?
– Gert
Commented Sep 6, 2019 at 13:35
• You cannot, for reasonable definitions. But I don't think that's what you mean. I think you mean "some simple formula like this"? If so, consider standard treatments generally ignore friction for clarity. Commented Sep 6, 2019 at 15:23
• I'm more concerned about adding another term to the original ODE. But I don't know what the term should be... That way I account for the magnetic field strength.
– JayP
Commented Sep 6, 2019 at 22:38