Deacon Dave wrote:
"Is it possible for a resonant condition to exist " (with a short
cable)?

If the cable is too short to enforce Zo, the source for Zload is not
necessarily a resistance and the load for the source can be resonant.

A short-circuited transmission line, shorter than 1/4-wavelength, is an
inductive reactance. An open-circuited transmission line, shorter than
1/4-wavelength, is a capacitive reactance.

A transmission line is not required for mismatch between source and
load. If a source can only supply a certain voltage to current ratio,
and it`s different from the immutable Zload, you have a mismatch and a
surplus of volts or amps which are rejected by the load.

The simple analysis of a series-resonant situation involving line
inductance and a load capacitance is that volts across either is (I)(Z).
The Z`s are about equal at resonanvce.

Trivia: 1/8-wavelength of line has a reactance which is equal to Zo.

Best regards, Richard Harrison, KB5WZI