= Solution
For positive <angular frequency>, the squared <amplitude> response of the <series-parallel RC band-pass filter> is
$$
|H|^2=\frac1{9+(w-w^{-1})^2}.
$$
Its denominator is minimized exactly when $w=w^{-1}$, so
$$
\boxed{\omega_0=\frac1{RC},\qquad H(\omega_0)=\frac13,\qquad
V_{\rm out}(t)=\frac{V_0}{3}\cos\omega_0t.}
$$
This is a <band-pass filter> maximum produced entirely by the two RC arms; the drawn <electrical circuit> contains no <inductor>. The low- and high-<frequency> limits are
$$
\boxed{H\simeq i\omega RC\quad(\omega\ll\omega_0),\qquad
H\simeq-\frac{i}{\omega RC}\quad(\omega\gg\omega_0).}
$$
Thus the output <amplitude> tends to zero linearly with $\omega$ at low <frequency> and as $1/\omega$ at high <frequency>. In real time,
$$
V_{\rm out}\simeq-V_0\omega RC\sin\omega t\quad(\omega\ll\omega_0),\qquad
V_{\rm out}\simeq\frac{V_0}{\omega RC}\sin\omega t\quad(\omega\gg\omega_0).
$$
The upper series <capacitor> suppresses low <frequencies>, while the lower shunt <capacitor> suppresses high <frequencies>.
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