What are the forces acting on a Pendulum Tuned Mass Damper? Upon researching tuned mass dampers, I came across this free body diagram of a pendulum tuned mass damper. However, I don't understand where many of the forces come from. What exactly are the forces acting on the mass and how do these equations represent them?



This is the link to the original paper. (diagram found on pg 34)
https://uwspace.uwaterloo.ca/bitstream/handle/10012/5776/Lourenco_Richard.pdf;jsessionid=47D13C2A1D7DB0B570CEDD9B9EB0273A?sequence=1
 A: He uses a non-inetrial reference frame, where the pendulum's bob is at rest, so there are two fictitious forces: the $$\text{centrifugal force} = mL(\frac{d\theta}{dt})^2$$, that acts radially and out, and the $$\text{Euler force} = $mL\frac{d^2\theta}{dt^2}$$ ,that acts tangentially. Then the tension, $T$, along $L$, the gravity vertically, a tangential force opposed to the motion, $\frac{c}{L}(\frac{d\theta}{dt})$ and an horizontal damping force oppossed to the motion, only acting in the horizontal direction. This last one is the one that troubles me because it should change direction as the pendulum moves, so I do not think this one is correct unless the damper moves up and down, so the force can remain horizontal. 
Also, the author decomposed all forces into the $x$ and $y$ components, and draw these components separately.
A: You can resolve this using the following FBD



*

*Tension in Pink

*Damping Forces (from linear and rotational dampers) in Red

*Inertial Forces in Gray. (Note: $\ddot{\theta}=\dot{\omega}=\alpha$)

