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R, L, and C are the values of resistance, inductance, and capacitance.
Circuit's impedance \( Z \) is given by:
\[ \boxed { Z = R + jX } \]$$ Z = R + j \omega L - j \frac{1}{\omega C} $$
$$ Z = R + j \left( \omega L - \frac{1}{\omega C} \right) $$
To satisfy the resonance condition, the circuit must be purely resistive. As a result, the imaginary part of the impedance is equal to zero:
$$ \omega L - \frac{1}{\omega C} = 0 $$
$$ \omega L = \frac{1}{\omega C} $$
$$ \omega^2 = \frac{1}{LC} $$
Angular frequency of the LC circuit:
\[ \boxed { \omega = \frac{1}{\sqrt{LC}} } \]Using \( \omega = 2 \pi f_0 \), we get:
$$ (2 \pi f_0)^2 = \frac{1}{LC} $$
Resonant frequency of the LC circuit:
\[ \boxed { f_0 = \frac{1}{2 \pi \sqrt{LC}} } \]
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