A fully charged capacitor C with initial charge Q _ 0 is connected...

The charge on the capacitor at any instant of time is

$Q = {Q}_{0}\cos \left(\omegat\right)$

$⇒ i = \dfrac{dQ}{dt} = - \omega{Q}_{0}$ \sin \left(\omegat\right)

\dfrac{1}{2} Li^{2} = \dfrac{Q2}{2C}$</p><p>${⇒ $\d$ dfrac{1}{2}L \left[\oomega{Q}_{0}\sin \left(\omegat\right)\right]}^{2} = $\dfrac{\left[{Q}_{0}\cos \left(\omegat\right)\right]2}{2C}$

\omega = $\dfrac{1}{LC}$

$⇒$\tan \left(\omegat\right) =$$1$

$\omegat = \tan^{- 1}\left(1\right) = \dfrac{\pi}{4}$

$t = \dfrac{\pi}{4\omega} = \dfrac{\pi}{4}\sqrt{LC}$