**Charge and Current Oscillations**

Since the differential equations are mathematically identical, their solutions must

also be mathematically identical. Because q corresponds to x, we can write the

general solution of by analogy to as where Q·is the amplitude of the charge variations, w is the angular frequency of the

electro magnetic oscillations, and cjJ is the phase constant. Taking the first derivative of with respect to time gives us the current of the LC oscillator = :; = -wQ sin(wt + cjJ) (33-13)

The amplitude / of this sinusoidally varying current is

/ = wQ, (33-14)

so we can rewrite E

Angular Frequencies

We can test whether Eq. 33-12 is a solution by substituting it and its

second derivative with respect to time into Eq. 33-11. The first derivative of Eq. 33-

12 is Eq. 33-13. The second derivative

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