How do I determine the impedance of Z in this circuit?
Using the voltage divider rule, 

$$\frac{V_2}{V_1} = \frac{R }{R + Z}$$

With measurement only at one frequency, you won't be able to determine \$r\$, \$L\$, or \$C\$, but if the goal is only to find \$Z\$, that doesn't matter.