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S.T an LC oscillator executes SHM and hence obtain an expression for the angular frequency of oscillation. |
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Answer» Solution :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)` 
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