In the following electrical network at `t lt 0`, key is placed on (1) till the capacitor got fully charged. Key is placed on (2) at `t = 0`. Time when the energy in both the capacitor and inductor will be same for the first time is

Explanation

At `t=0` , change on capacitor `q_(0)=CE`
Change on capacitor in terms of `t`
`q=q_(0)cosomegat` , `omega=(1)/(sqrt(LC))`
`U_(L)+U_(C)=(q_(0)^(2))/(2C)`
`U_(L)=U_(C)`
`2U_(C)=(q_(0)^(2))/(2C)` implies `U_(C)=(q_(0)^(2))/(4C)` implies `(q^(2))/(2C)=(q_(0)^(2))/(4C)`
`q=(q_(0))'/(sqrt(2))`
`q=q_(0)cosomegat`
`(q_(0))/(sqrt(2))=q_(0)cosomegat` implies `cosomegat=(1)/(sqrt(2))=cos(pi)/(4)`
`omegat=(pi)/(4)` implies `t=(pi)/(4omega)=(pi)/(4)sqrt(LC)`