Explain how $LC$ oscillations take place in the circuit.

(N/A) An $LC$ circuit consists of a capacitor with capacitance $C$ and an inductor with inductance $L$.
$1$. Initially,the capacitor is charged to a maximum charge $q_m$. The electrical energy stored in the capacitor is $U_E = \frac{1}{2} \frac{q_m^2}{C}$. Since the circuit is open,the current $I = 0$,and the magnetic energy in the inductor is $U_B = 0$.
$2$. When the switch is closed at $t = 0$,the capacitor begins to discharge. As the current $I$ flows through the inductor,it creates a magnetic field,and magnetic energy $U_B = \frac{1}{2} LI^2$ begins to build up.
$3$. At $t = \frac{T}{4}$,the capacitor is fully discharged $(q = 0)$,and the current reaches its maximum value $I_m$. All the energy is now stored in the magnetic field of the inductor: $U_B = \frac{1}{2} LI_m^2$.
$4$. After this,the current continues to flow due to the back $EMF$ of the inductor,charging the capacitor with opposite polarity. This process continues,leading to continuous oscillations of energy between the electric field of the capacitor and the magnetic field of the inductor.