In this article bending control of rotating Euler-Bernoulli beam is considered. It is assumed that the fixed-free elastic beam is attached to a servomotor using a variance constrained controller, specifically output variance constrained controller for vibration suppression. Equations of motion of the system obtained via Hamilton's principle and Galerkin method are used. The resulting linearized state-space models obtained considering just one or three modes are used for control system design. Output variance constrained controllers are designed in order to control bending at the beam tip and beam rotation angle with different variance constraint magnitudes. Closed-loop responses are analyzed when they experience white noise perturbations. Comparisons between system having tighter variance constraint and weaker variance constraint are also performed. Finally, robustness of Output variance constrained controllers with respect to the modeling uncertainty (i.e. variation of number of modes) is examined.