= Lorentz oscillator model
{c}
A bound charge obeying $m\ddot u+m\gamma\dot u+m\omega_0^2u=qE$ gives a resonant <electric susceptibility>. For <carrier density> $n$ and the $e^{-i\omega t}$ convention,
$$
\epsilon_r(\omega)=1+\frac{\omega_p^2}{\omega_0^2-\omega^2-i\gamma\omega},\qquad
\omega_p^2=\frac{nq^2}{m\epsilon_0}.
$$
Positive damping gives $\operatorname{Im}\epsilon_r\geq0$ for $\omega>0$, expressing passive absorption. Independent resonances add to the <electric susceptibility>. Setting $\omega_0=0$ gives the <Drude frequency response>.
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