Q.Two magnets with the same dimensions and mass, but of magnetic moments μ₁ = 100 A m² and μ₂ = 50 A m² are jointly suspended in the earth's magnetic field so as to perform angular oscillations in a horizontal plane. When their like poles are joined together, the period of their angular S.H.M. is 5 s. Find the period of angular S.H.M. when their unlike poles are joined together.

Angular (or torsional) S.H.M. extends the same ideas to a system oscillating in angle rather than displacement: a body -- for instance a disc suspended centrally from a twisted wire, or a bar magnet freely suspended in a uniform magnetic field -- experiences a restoring TORQUE proportional to its angular displacement theta and opposite in direction to it, tau = -ctheta, where c is the restoring torque per unit angular displacement. Using tau = I(d^2theta/dt^2) (I = moment of inertia about the axis of rotation), this gives the angular-S.H.M. differential equation I*(d^2theta/dt^2) + ctheta = 0, structurally identical to the linear-S.H.M. equation with theta replacing x, I replacing m, and c replacing k. The period follows the same general template, T = 2pi*sqrt(I/c). …