Charge and Current Oscillations

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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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