Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.
First convince yourself using a dimensional analysis.
Then of course you will get (w0)^2=1/(LC)
When the external frequency (w) is equal to the natural frequency (w0), the term in the parenthesis vanishes and Z =R (resistive)
When external freq w is much greater than w0, Z is apparently inductive and when w is much smaller than w0, Z is apparently capacitive.