Electronics Fundamentals/Electronic Oscillator/Sinusoidal Wave Oscillator

Sinusoidal Wave Oscillator
Sinusoidal Wave Oscillator is an Electronics device that generate Sinusoidal Wave Oscillation

Configuration
LC connected in series has the capability to generate Sinusoidal Wave Oscillation at equilibrium

Mathematical Analysis

 * $$L \frac{d}{dt} i + \frac{1}{C} \int i dt = 0$$
 * $$\frac{d}{dt} i + \frac{1}{LC} \int i dt = 0$$
 * $$s^2 + \frac{1}{LC} = 0$$
 * $$s = \pm j \sqrt{\frac{1}{LC}} t$$
 * $$s = \pm j \omega t$$
 * $$i = e^(j \omega t) + e^(-j \omega t)$$
 * $$i = A Sin \omega t$$
 * Wave-he.png

Summary
LC series has the capabilty to generate oscillation of sinusoidal wave oscillate at frequency
 * $$\omega = \sqrt{\frac{1}{LC}}$$