Galvanometer readout of an induction pulse ($J_g\ddot{\theta }+b_g\dot{\theta }+{\kappa }_g\theta =K_{g}i$)

A small-angle galvanometer model combines its moment of inertia $J_g$, damping coefficient $b_g$ and restoring coefficient ${\kappa }_g$ with a torque per electric current $K_g$. The resulting damped harmonic oscillator responds to the current pulse through the displayed equation. Its angular deflection $\theta$ can continue after the driving electric current has ceased. Inferring the current's detailed time dependence requires the instrument response, rather than equating needle angle with instantaneous current. This is a generic readout model, not a calibration of Faraday's historical instrument.