= Solution
An unbound conduction <Electron> has no local restoring force, so set $\omega_0=0$ while retaining inertia and <momentum relaxation time> $\tau=1/\gamma$. This is the <Drude model>:
$$
\boxed{\epsilon_r(\omega)=1-\frac{\omega_p^2}{\omega(\omega+i\gamma)}.}
$$
Separating the response gives
$$
\boxed{\epsilon_r'=1-\frac{\omega_p^2}{\omega^2+\gamma^2},\qquad
\epsilon_r''=\frac{\omega_p^2\gamma}{\omega(\omega^2+\gamma^2)}.}
$$
For a good <metal>, $\gamma\ll\omega_p$. The real part is strongly negative at low frequency, crosses zero at $\sqrt{\omega_p^2-\gamma^2}\simeq\omega_p$, and approaches one from below. The imaginary part diverges as $\omega_p^2/(\gamma\omega)$ at low frequency, reflecting the finite dc <electrical conductivity> $\sigma_0=\epsilon_0\omega_p^2/\gamma$, then decays as $\omega^{-3}$. The low-frequency imaginary response describes conduction loss, not a finite-frequency bound-electron absorption line. Core-electron and interband responses can add a background in a real metal.
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