The paper must be considered as a contribution to the control of the vibrating string. The authors propose an algebraic linear system for the Mikusiński operators to solve a problem for the Euler-Bernoulli flexible beam. They consider the motion of a flexible beam of length \(R\), embedded at the extremity \(x=0\) in a rotating axis and solitary at the extremity \(x=R\) with a point mass \(m\). They prove the existence of an optimal control and determine the trajectory of a stabilizing control.