Viscous vibration damping of torsional oscillation

A method of damping torsional vibrations in a borehole string, the method comprising:

• disposing a rotatable downhole component and a damping assembly in a borehole in a subsurface formation, the damping assembly including a cavity that is rotationally fixed relative to the rotatable downhole component, and an inertial mass disposed in the cavity and coupled to the rotatable downhole component by a damping fluid disposed between the inertial mass and the rotatable downhole component, wherein the inertial mass is free to move relative to the rotatable downhole component;
• performing an operation that includes rotating the rotatable downhole component and causes the torsional vibrations of the rotatable downhole component;
• and
• damping at least partially the torsional vibrations of the rotatable downhole component, wherein the damping includes causing rotational acceleration to be reduced based on shear occurring in the damping fluid due to relative movement between the inertial mass and the rotatable downhole component.