Practical Electronics/Sin Wave Oscillator

With an LC series

$L\frac{dI}{dt}+\frac{1}{C}\int Idt=0$

$\frac{d^{2}I}{dt}+\frac{1}{LC}I=0$

$\frac{d^{2}I}{dt}+\frac{1}{LC}=0$

$\frac{d^{2}I}{dt}=-\frac{1}{T}$

$I=A{e}^{\pm j\omega t}=A\sin \omega t$

The reponse of an LC series is a Sinusoidal Wave or LC series can be used to produce Sin Wave Oscillator