"Wait a min -- I thought centripetal force was the "real" force (what
keeps the bob from observing the 1st law, and c-fugal was the frame force
(pseudo or unreal force)."
Yes, of course I should have stated that "centrifugal" force arises in a
non-inertial reference frame!
Still I would claim that there is no centripetal force as such; it is just a
nickname for a sum of real forces acting in the normal direction.
Who could explain what is the rationale behind the TPT derivation which talks
about centripetal force as an extra real force in addition to tension and
weight?