FYKOS Year 37 Series 6 Problem 5 — oscillating magnets · FYKOS 37 #37.6.5
Physics · mechanics · electromagnetism
Problem
Consider two identical dipole magnets, which we fix so that they can rotate in
the same plane without friction (their axes of rotation are parallel). If we
deflect the magnets slightly out of their equilibrium position, they begin to
oscillate. Find the eigenmodes of these oscillations and calculate their
frequencies. Discuss what the motion of the magnets will be like for general
initial deflection (you don't have to explicitly calculate this case). The
magnets have a magnetic moment m, a moment of inertia about the axis of
rotation J and the mutual distance between their centers is r.