Bridged T-network equation

Question

This and a couple of other Q's have been driving me mental, and i can't wait to see if i got them right. Any input would be massively appreciated. Cheers.

S= R/(w^4)(L^2)(C^2) j[2/wC - 1/(w^3)(LC^2)]

If the imaginary term equates to zero, show that the equation can be re-written as;

R=S/4

Answer 1

w^2 = 1/LC

That equation is common.  It defines a resonant frequency of circuits.  but I can't figure out where the 1/4 factor comes from.

f = 1/(2pi*sqrt(LC)), but even in this case the factor would be 1/4pi^2, not 1/4.