Yes, it sounds like you come at this from an engineering background, whereas I come from a physics one. So our way of thinking about it may differ. No matter, I’ll just be more careful in my exposition.

So the equation for a simple harmonic oscillator derived for a pendulum is a second order differential equation with angular frequency given by /sqrt(g/L). If you add another force on the side, this will modify this equation to yield an angular frequency of /sqrt([g-g’]/L), where g’ is the acceleration from the lead weight: GM/d^2.

Question:

Do you agree that if I put more mass above my pendulum it will slow down, and if I put more mass below it, it will speed up, and that at the correct position besides it, more mass would neither slow it nor speed it?

For the drag, yes you pumped the jar, but it is not a pure vacuum in there, right?

Yeah, probably a 99% vacuum. My micron vacuum gauge is on loan to a friend at the moment, but my HVAC pump does a pretty good job.

Good enough that a goose down feather falls like a BB and bounces in the vacuum. So I would say the drag on my round dense tungsten weight is probably quite minimal.

You just reduced the air density beyond the precision of your psi meter. Achieving a near vacuum is an expensive and time consuming process requiring heat pumps, throttling techniques, and some others I do not recall at the moment. So your drag is reduced, but not absent. Since the force you attempt to measure is very small, are you certain that the drag has been reduced enough? It could be that the drag is still the same order of magnitude as the effect you purpose to measure. That’s why checking this is useful.

You may be missing the entire underlying principle of my experiment.

Drag primarily causes loss of efficiency. The pendulum just won't swing as long on it's own if there's too much drag. But the frequency will still be rather stable because it's primarily determined by the length of the pendulum and the force acting upon it.

So if I can maintain constant drag (by having it in a vacuum jar) and constant pendulum length, then the only other major variable is the gravitational force in the vertical axis.

Now of course there are other small effects, temperature can change the length of my aluminum pendulum shaft, light can create a photoelectric effect and charge up my pendulum, and so on and so on.

And a shift in local level (like if the table it's on gets tipped a bit) might upset the frequency a little due to the fact that the moment at which the excitation pulse is fired will actually not be centered in the swing.

But my plans are, Lord Willing, to actually move it to a place where it's bolted down to a 2000 pound steel machine that's sitting on concrete, and put a light shield around it to reduce possible outside influences.

But anyway, even if there is drag, the frequency is still primarily a function of pendulum length and gravitational force in the vertical axis.

So by taking a long reading without the lead weights under it then another long reading with the lead weights under it, without changing the drag or anything else, then I should be able to get a difference in frequency and from that calculate the difference in gravitational force.

Does that make sense?

Can you see how the effect of the drag would be self-canceling, and it's really a differential measurement where gravitational force is the only major input variable?

And if you have a better idea for measuring gravity I'm all ears!