Stefan Wolfe wrote:

Hello Art, this is an easy one that any amateur could answer and which I
would think is well below your level of the physics (so the reason for your
question confuses me): If the antenna is perfectly resonant, then it, as a
total charge distribution system or "circuit", has a time constant of zero.
At any point along the length of the antenna, there are time constants that
could apply, RC or R/L depending upon reactivity of the section in question.
But you are asking about the distributed capacitance; what does that mean,
let's say in terms of any point at a designated distance from feed point?
Where do you want to calculate the time constant? Otherwise, once the
antenna is resonant either by design or by the addition of reactive
components (such as a coil in the center), as a whole it is a resonant
circuit where reactive impedances cancel out and you are only left with
resistance (ohmic + radiation resistance) and the time constant of the whole
circuit must be zero.

In a resonant circuit containing R, L, and C, there most definitely is a
time constant. Related to Q, it describes the time taken for the circuit
to respond to a transient. The higher the Q, the longer the time
constant, and the longer it takes the circuit to come to equilibrium
after a step or sinusoid is applied, and to decay after it's removed.
Failure to understand this has resulted in some very poorly designed
audio filters for CW, among other things.

The reactances in a resonant circuit cancel only at a single frequency.
That means if you apply a sinusoidal signal at the resonant frequency
for a very long time, and don't change anything about it (phase,
amplitude, frequency, or waveshape), the resonant circuit will act like
a resistor. But it won't under any other circumstances. As soon as you
say "time constant", you're speaking of the response to a changing, not
steady state sinusoidal, signal. And the response of the resonant
circuit containing L and C to any change in the signal will be very
different from the response of a resistor. And it will exhibit a time
constant. (This can bee seen in the time domain equations for i(t) and
v(t) which contain an exponential term multiplying the sinusoidal term.
The time constant is in the exponent. See any text on electrical
circuits for more detail.)

Roy Lewallen, W7EL