solution
solution.
Suppose the inductor and capacitor in the LC oscillator circuit in Fig. 8.22 are not ideal, but instead have some small resistance that can be lumped together. Assume that V = 10 V, Rs = 25 Ω, L = 5 nH, and C = 2 pF, just as in Problem 8.66. Suppose the resistance associated with the inductor and capacitor is 10 mΩ.
 a) Calculate the values of the neper frequency, a, and the resonant radian frequency, v0.
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Order Paper Nowb) Is the response of this circuit overdamped, underdamped, or critically damped?
 c) What is the actual frequency of oscillation, in GHz?
 d) Approximately how long will the circuit oscillate?
Problem 8.66
a) Suppose the circuit in Fig. 8.22 has a 5 nH inductor and a 2 pF capacitor. Calculate the frequency, in GHz, of the sinusoidal output for t ≥ 0.
b) The dc voltage source and series-connected resistor in Fig. 8.22 are used to establish the initial energy in the inductor. If V = 10 V and Rs = 25 Ω, calculate the initial energy stored in the inductor.
 c) What is the total energy stored in the LC circuit for any time t ≥ 0?
Fig. 8.22
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