A charged 30μF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

Capacitance, C = 30μF = 30 x 10⁻⁶F

Inductance, L = 27 mH = 27 x 10^-3 H

Angular frequency is given as:

ω_r = 1 /√(LC) = 1/√ ( 27 x 10^-3 x 30 x 10⁻⁶  )

= 1/ (9 x 10⁻⁴ ) rad/s

= 1.11 x 10³ rad/s

Hence ,the angular frequency of free oscillations of the circuit is 1.11 x 10³ rad/s