Answer
a. $\omega = \frac{1}{\sqrt{ LC}} $.
b. 7560 rad/s, $37.8 \Omega$.
Work Step by Step
a. Equate the reactance of the capacitor to that of the inductor and solve for the angular frequency.
$$\frac{1}{\omega C}=\omega L$$
$$\omega = \frac{1}{\sqrt{ LC}} $$
b. Use the numbers given in the problem.
$$\omega = \frac{1}{\sqrt{ (5.00\times10^{-3}H)( 3.50\times10^{-6}F)}}=7560 rad/s $$
$$\frac{1}{\omega C}=\omega L=37.8 \Omega $$
