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[Zeitmaschine]

Expand on your reasoning why we land up with "a bowl and one olive" and the weight thereof. 

This is because the ball in the bowl behaves like a pendulum. It is a pendulum without a string.

The Finsrud and Milkovic are an other chapters for discussion, I didn't go there.

Milkovic is a short trip to go. Explanation:

2 is a lever rotating around the pivot 3 and normally it rests on the left side on the anvil 1 due to the overbalance on that side.

Supposed a weight of 10 Kg is needed on the right side to move the left side up. Then each time we want to do a hit with that lever against the anvil we have to push down the right side with a force of 10 Kg and then release it.

Now we attach a 10 Kg weight 4 to that right side. Then the left side of the lever comes up and stays there. But we are to lazy to remove that weight each time we want back the overbalance on the left side in order to hit against the anvil.

Hence we swing that 10 Kg weight like a pendulum. Each time the pendulum reaches one of its upper positions, the 10 Kg weight becomes weightless and therefore the lever hits the anvil due to the momentarily regained overbalance on the left side.

All energy we need to do this is the energy needed to overcome the friction of the pendulum (instead of removing that 10 kg weight).

Any further questions?

[minnie]

   What you need is a brachistochrone!!

[Red_Sunset]

This is because the ball in the bowl behaves like a pendulum. It is a pendulum without a string.
Milkovic is a short trip to go. Explanation:
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Any further questions?

The pendulum topic has been investigated quite thoroughly over the past years.
My further question:   and now, what do we do  ?

[Red_Sunset]

An eccentrically flywheel (vibrator driven by a motor) has absolutely nothing to do with the state of weightlessness of a pendulum's bob!
This is another wrong statement. At the turning point of the bob there is nothing. No weight, no centrifugal force, no centripetal force. The bob (even if a few tons) hovers in zero gravity for a moment in time. And essentially that's the kick when swinging in a children's swing.
Then how do you explain the principle of work of the Finsrud and the Milkovic devices? They are proven to generate OU.
As we can see, the magic fortunately does not disappear.

Zeit,

What energy is causing that periodic bending of that beam?

Let me get back to my reply #72,  where the main point of the post was to link the moving pivot pendulum to the eccentric motor which I gather was not wholly understood.  No complicated math, just plain logic

Let me expand in layman's terms,
The pendulum can be seen as sling (weapon) when used in rotary fashion. It sure is now no pendulum any longer but the centrifugal and centripetal physical properties are the same as the pendulum when the weight is at a certain velocity. At that point the rotating sling shot finds equivalency to a motor with an eccentric weight (your standard vibrator).
When loosely mounted vibrator axle makes a circular path during the eccentric weight rotation, the radius of this circle is equivalent to "bending top bar".
What effectively happens is the the rotational radius path of the eccentric weight is no longer the radius as with a fixed axis position, it is now "weight radius + axle radius".  The effect rotating weight radius has now expanded and therewith stores more energy.  That energy comes from the shaft. 
This is easy to proof by measuring the current consumption of a small vibrator motor, holding the motor fixed, versus allowing it to vibrate.
No complicated math, just plain logic, "Vibration consumes more input power" = "Bending of the beam consumes more input power "

Greetings, Red_Sunset

[MarkE]

Strange. The ball goes into freefall (accelerating at a rate of 9.8 m/s/s) after reaching its apex (although a minimum of deflection occurs already at the beginning) and to the best of my knowledge a body in freefall is weightless.

Yes, I agree for the one instant at the start of the fall, it accelerates at 1G and there is no apparent reaction force, IE it is weightless at that one instant.