S.T an LC oscillator executes SHM and hence obtain an expression for the angular frequency of oscillation.

Explanation

Applying KVL we get,
`v_(c)-L(di)/(dt)=0`
i.e, `(q)/(C)-L(di)/(dt)=0`
`therefore i=-(dq)/(dt),(di)/(dt)=(-d^(2)q)/(dt)`
`therefore (q)/(C)+L(d^(2)q)/(dt^(2))=0`
or `(d^(2)q)/(dt^(2))+(1)/(LC)q=0` which is similar to `(d^(2)x)/(dt^(2))+omega_(o)^(2)x=0`
`therefore omega_(0)^(2)=(1)/(LC)`
i.e., `omega_(0)-(1)/(sqrt(LC))andq=q_(m)cos(omega_(0)t+phi)`