Anti-Vibration Technology

[Toolmaker51]

That's a very good deduction, I'm no physics major, but it visualizes well enough. There always seems a vibration feels more pronounced at one spot, usually not midpoint. Certainly mechanical conditions alter what vibrations would do on their own.
And why some boring bars have a taper that work well, while others might have taper yet can't generate a decent cut. It's worse in unprogrammed milling machines; having limited feed rates compared to any lathe.

[machining 4 all]

Remarks:
*The delay comes from the Newton's second law: F = m a = m (dv/dt). The "dt" argument introduces the "delay", or better a time shifting factor in the transfer function of the motion from workpiece on the spindle (in the case of the lathe) to the boring bar holder. We can use this transfer function to assess the stability of the system composed by the workpiece in rotation (as action) and the boring bar (as reaction) and a noise generator determined by the point of contact of the tool with the workpiece. This noise will induce oscillations that could increase in aplitude if the system resonates (i.e., it's not stable).
N.B. This is to explain my intuition, I do not know if this is the common way to model a system like this.

M4A says: The correct solution for this mass-spring system is...

[tonyfoale]

The principle shown in the video seems to be different than filling the boring bar with lead. The latter increases the mass, the former induce a dumpening due to the internal mass but mediated through the elastic rings. .

The lead does more than add mass, it is exceptionally good at adding damping.

[Toolmaker51]

This keeps rolling around the old bean;
Even if a molten lead plug shouldn't adhere, plugging the end to restrict movement, still dampens naturally in what little space it does have. Lead probably has no significant harmonics. Back-filling a viscous fluid would be very effective.

[nova_robotics]

Remarks:
*The delay comes from the Newton's second law: F = m a = m (dv/dt). The "dt" argument introduces the "delay", or better a time shifting factor in the transfer function of the motion from workpiece on the spindle (in the case of the lathe) to the boring bar holder. We can use this transfer function to assess the stability of the system composed by the workpiece in rotation (as action) and the boring bar (as reaction) and a noise generator determined by the point of contact of the tool with the workpiece. This noise will induce oscillations that could increase in aplitude if the system resonates (i.e., it's not stable).
N.B. This is to explain my intuition, I do not know if this is the common way to model a system like this.

M4A says: The correct solution for this mass-spring system is...

Yeah but that only applies to undamped systems that are allowed to naturally oscillate. There is damping when the tool touches the workpiece, or when you use fancy boring bars with lead and grease in them. As soon as you start using the tool you have to take damping into account.

[Claudio HG]

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M4A says: The correct solution for this mass-spring system is...

Thank you for the solution for mass-spring, here however we have an active motion (either propelled by a motor or by human labour). Anyway even with the mass-spring the time enters into account: ω = 2 π f; where f = 1 / t.

[Claudio HG]

The lead does more than add mass, it is exceptionally good at adding damping.

Well, I agree that lead has some kind of dumping properties, that's because lead has a very low modulus of elasticity (14GPa, lower than concrete which is 30GPa), and with one of the most larger mass. But grease and (probably) those rings have even lower modulus of elasticity, for instance rubber has ~ .1 GPa.