This paper continues the senior author’s previous investigation of the slowly
rotating Timoshenko beam in a horizontal plane whose movement is controlled by
the angular acceleration of the disk of the driving motor into which the beam is rigidly
clamped. It was shown before that this system preserves the total energy. We consider
the problem of stability of the system after introducing a particular type of damping.
We show that the energy of only part of the system vanishes. We illustrate obtained
solution with the critical case of the infinite value of the damping coefficient.