Q.Write the differential equation for angular S.H.M.

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). …