Give the qualitative explanation of the action of an LC oscillator in the absence of any external ac voltage source. Assume that the capacitor is charged initially.

Explanation

(i) At t = 0, the capacitor has energy of `(1)/(2)(q_(m)^(2))/(C)`. Energy associated with the inductor is zero.
When the switch is closed, capacitor discharge, magnetic energy gets stored in the inductor. When the current reaches its maximum value `i_(m)("at "t=(T)/(4))` all the electrostatic energy is converted into magnetic energy in the inductor. Magnetic energy `-(1)/(2)Li_(m)^(2)`. Energy in the capacitor becomes zero.
(ii) During the time interval from `t=(T)/(4)` to `t=(T)/(2)`, the current starts charging the capacitor until it gets fully charged `("at "t=(T)/(2))`. The polarity of the capacitor will be opposite. Energy in the inductor become zero.
(iii) During the time interval from `t=(T)/(2)` to `t=(3)/(4)T`, the inductor gets the current from the capacitor, until the inductor gets the maximum current and maximum energy `((1)/(2)Li_(m)^(2))` is stored in the inductor.
(iv) During the time interval from `t=(3)/(4)T` to `t=T`, the initial polarity of capacitor gets restored and charging the capacitor to acquire energy of `(1)/(2)(q_(m)^(2))/(C)`
This process of conversion of electrostatic energy to magnetic energy takes place without any external source voltage as long as the oscillating system does not lose energy in the form of heat or electromagnetic energy.
(i) at t = 0

(ii) at `t=(T)/(4)`

`(T)/(4)lt t lt (T)/(2)`

(iv) at `t=(T)/(2)`