You can use the Rigid Body setup pane to create delays or to smooth jerky movements in animation created by constraints.
Create a Rigid Body constraint. See Using a constraint to create a Rigid Body for more information.
Once you have assigned Source and Constrained objects to a Rigid Body constraint, click the Setup tab in the Constraint settings.

Rigid Body Setup pane
Enter a value in the Time Before Recovery field.
Enter a value in the Recovery Damping Time field.
MotionBuilder measures these fields in frames per second or timecode format, depending on the settings in the Global Controls.