This puzzled me since yesterday as I discovered how the suspension of
pendulum clocks is made, that is a springy plate.
There is less loss in a suspension like that than there would be in a pivot
bearing.
The spring doesn't change parameters as it gets dirty or the oil dries out.
-following the above, the lenght of the pendulum varies during a swing,
Ok that we can neglect the above yet having an extremely good approximation,
but is it conceptually right?
With a constant length pendulum, there is a slight variation in the frequency
with the height (width?) of the swing. (I haven't done the math since
college physics which was a long time ago.)
It would be interesting to see how much the length of a pendulum changes as
the suspension spring bends and how much that changes the resonant frequency
and how that compares with the length change due to temperature. I suspect
it's down in the noise.
--
These are my opinions. I hate spam.