A rotary machine comprising an apparatus for balancing a rotor therein, said rotary machine comprising: a rotor comprising a hub, at least two rotor blades coupled to said hub, and a rotor shaft (28, 30) coupled to said hub for rotation therewith; at least one blade pitch actuator coupled to said at least two rotor blades for controlling an angle of pitch of said at least two rotor blades; at least one sensor (48, 50) configured to measure at least one of a load, an acceleration, and a displacement that pertains to a mean value of one or more bending moments acting on said rotor shaft; and a processor coupled to said at least one blade pitch actuator and coupled to said at least one sensor (48,50), said processor configured to balance said rotor by: receiving, from said at least one sensor, at least one measurement of either a load, an acceleration, or a displacement that pertains to at least one of said mean value bending moments acting on said rotor shaft (28,30); determining said mean value of the one or more bending moments acting on said rotor shaft (28,30) based, at least in part, on the received at least one measurement over a predetermined amount of time; and determining a pitch offset angle value for at least one rotor blade that facilitates reducing the mean value of the one or more bending moments acting on said rotor shaft (28,30). a rotor comprising a hub, at least two rotor blades coupled to said hub, and a rotor shaft (28, 30) coupled to said hub for rotation therewith; at least one blade pitch actuator coupled to said at least two rotor blades for controlling an angle of pitch of said at least two rotor blades; at least one sensor (48, 50) configured to measure at least one of a load, an acceleration, and a displacement that pertains to a mean value of one or more bending moments acting on said rotor shaft; and a processor coupled to said at least one blade pitch actuator and coupled to said at least one sensor (48,50), said processor configured to balance said rotor by: receiving, from said at least one sensor, at least one measurement of either a load, an acceleration, or a displacement that pertains to at least one of said mean value bending moments acting on said rotor shaft (28,30); determining said mean value of the one or more bending moments acting on said rotor shaft (28,30) based, at least in part, on the received at least one measurement over a predetermined amount of time; and determining a pitch offset angle value for at least one rotor blade that facilitates reducing the mean value of the one or more bending moments acting on said rotor shaft (28,30). receiving, from said at least one sensor, at least one measurement of either a load, an acceleration, or a displacement that pertains to at least one of said mean value bending moments acting on said rotor shaft (28,30); determining said mean value of the one or more bending moments acting on said rotor shaft (28,30) based, at least in part, on the received at least one measurement over a predetermined amount of time; and determining a pitch offset angle value for at least one rotor blade that facilitates reducing the mean value of the one or more bending moments acting on said rotor shaft (28,30).