= Solution
Take $q=-e$ as the signed electron charge. The <Lorentz oscillator model> is a driven damped bound charge:
$$
\boxed{m\ddot{\mathbf u}+m\gamma\dot{\mathbf u}+m\omega_0^2\mathbf u=q\mathbf E(t).}
$$
The first term is inertia, the second is a phenomenological frictional loss of coherent motion to other degrees of freedom, and the third is the linear restoring force from binding to the atom. The driving term is the <electric force>. The natural <angular frequency> $\omega_0$ represents the <electronic transition>; this classical oscillator describes its near-resonant <linear response>. The friction convention is $m\gamma\dot u$, so no factor two is hidden in $\gamma$.
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