Here is an example of an LC circuit, where a charged capacitor is connected to an inductor. The beauty of this circuit is that one can start an oscillating current (AC current). This is the same as 'shaking' electrons, and this means electromagnetic waves are produced in the E-and B-fields. These waves travel at the speed of light. We will see that the math produces the same second-order differential equation we have in simple harmonic motion of oscillating springs! So sines and cosines are the solutions to this equation. Check it out!
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