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## Homework Statement

In the circuit below, find the resonant frequency ([itex]\omega_0[/itex]) and [itex]Z_{IN}\left(\omega_0\right)[/itex].

http://img143.imageshack.us/img143/9845/problem1444dx4.jpg [Broken]

## Homework Equations

[tex]\omega_0\,=\,\frac{1}{\sqrt{LC}}[/tex]

## The Attempt at a Solution

The resonant frequency is easy to find:

[tex]\omega_0\,=\,\frac{1}{\sqrt{20mH\,9\mu F}}\,=\,2357\,\frac{rad}{s}[/tex]

Now I reconfigure the circuit a little to combine the resistor and capacitor into the element [itex]Z_1[/itex]:

http://img156.imageshack.us/img156/4173/problem1444part2hm4.jpg [Broken]

Does that seem right?

Now I get this:

[tex]Z_{IN}\,=\,\frac{1}{1\Omega}\,+\,\frac{1}{j\omega\,0.02}\,+\,9X10^{-6}j\omega\,+\,10[/tex]

[tex]Z_{IN}\,=\,\frac{1}{j\omega\,0.02}\,+\,9X10^{-6}j\omega\,+11[/tex]

Now what do I do?

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