Anti-Vibration Technology

[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.