Eddy Current Braking of a Simple Pendulum

[edosmond]

I'm setting up an experiment and I 'd like to somehow quantify the effects of magnetic braking on a simple pendulum.

At the moment, I have a curved sheet of Aluminium that I will swing freely between two magnets set up in yoke (horseshoe magnets). The magnets induce eddy currents in the aluminium and cause damping. I also have an Aluminium sheet that has slits cut in it to remove the eddy currents, and I want to compare the two pendula.

The problem is, I'm not well versed in anything like this other than very 'ideal' pendula i.e. with no resistance and I'm struggling to think of a way to quantify the difference between the behaviour of the two pendula. So far my research has only uncovered very complicated differential equations involving damping coefficients and damping ratio.

Need to start tomorrow, any thoughts?

 

[Vailanor]

One way to quantify the difference in behaviour between the two pendula is to measure the time it takes for each pendulum to reach its maximum swing from a resting position. This can be done by timing the swing from start to finish and then measuring the amplitude of the swing. By comparing the two times, you can get an indication of the effects of the magnetic braking on the pendulum's motion. Another way to quantify the difference in behaviour between the two pendula is to measure the period of oscillation of the pendulum. This can be done by measuring the time it takes for the pendulum to complete one full cycle of oscillation (from one maximum swing to the next). By comparing the two periods, you can also get an indication of the effects of the magnetic braking on the pendulum's motion. Lastly, you could also measure the damping ratio of the pendulum. This can be done by measuring the amplitude of oscillation at successive times, and then using the damping ratio equation to calculate the damping ratio. Comparing the damping ratios between the two pendula can give you a more accurate indication of the effects of the magnetic braking on the pendulum's motion.