Considering a set up where a conducting pendulum oscillates between two permanent magnets, I want to somehow calculate the power dissipated by the magnetic braking force the magnets provide, in order to predict the time it would take for the pendulum to loose it's energy and come to rest. I read some articles on Joule's law, which states that P=I^2 * R, which is the rate of increase of internal energy of the conductor. However on wikipedia, I found a different equation for power dissipation of eddy currents which I've attatched:
Firstly, in the second formula, what does the frequency refer to? Second, which of these formulas would I use in this case? Also, How would I go about predicting the time it would take for the damping force to remove all energy from the conductor, since the force only applies at times when the pendulum is leaving the magnetic field? This is my first time using this website so apologies for any rules I've broken, I'm only a highschool student.
