I have been an assignment to design a "double zobel" network.

The first image is Part 1 of the assignment. It's instructions are to prove the Z(in) is purely resistive for the circuit shown. Based on the fact that R=8 ohms and L =400uH, I have calculated C to be 6.25uF.

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I believe I have done part 1 circuit analysis correctly. I was able to show Z1 as (8-8i) and Z2 as (8+8i), indicating resonant frequency. I also calculated Z(in) to be 8ohms and purely resistive. If anyone sees any problem with my work in Part 1, please let me know.

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The third image I have shown is the LTspice build of the circuit. Along with the circuit build, i have run an ac analysis using a 1A current, in and have measured for V(in). My assumption was that since Z=V/I, if I sent I=1, then Z=V, so whatever I measured for the input voltage would equal my impedance, which shows at 8V, same as the 8ohm impedance. Is there a way to run the spice analysis at resonant frequency so that I can show a purely real result?

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Part 2 is where I am struggling. I really honestly don't even know where to begin other than plugging random numbers into LTspice. The purpose is to design a network based on the circuit shown and the values given that would result in a purely real and purely resistive input.

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My first problem with this circuit is how you would even go about determining a resonant frequency, given that you have so many unknown values, and I don't know which values of L and C to plug into the formula, because there is more than one L and more than one C. I have played around in LTSPice, and came up with a circuit that appears to be purely resistive, and Vin is close to Vout, but it is not purely real, and I don't know how to make it both without simply guessing. Is there a way to use circuit analysis to solve this problem?

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Thank you for reading. I will be here all day to take advise.