If a series LCR. circuit is connected across the terminals of an electric generator that p...

If a series LCR. circuit is connected across the terminals of an electric generator that pro­duces a voltage V = V0eiωt, the flow of electrical charge q through the circuit is given by the following second-order differential equation:

(a) Verify the correspondence shown in Table 3.6.1 between the parameters of a driven mechanical oscillator and the above driven electrical oscillator.

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(b) Calculate the Q of the electrical circuit in terms of the coefficients of the above differ­ential equation,

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(c) Show that, in the case of small damping, Q can be written as Q = R0/R, where R0 = √L/C is the characteristic impedance of the circuit.