Dear Tejas,
The equation you’ve identified in your presentation represents the natural frequency of a drivetrain with a rigid rotor in a free-free condition. When comparing to the FAST results from Campbell Diagram & MBC3 output relation, I see a few problems:
*The FAST linearization from Campbell Diagram & MBC3 output relation represents a fixed-free condition (the generator DOF is disabled, GenDOF = False).
*The FAST linearization from Campbell Diagram & MBC3 output relation includes flexible blades (the rotor is not rigid, FlapDOF1 = FlapDOF2 = EdgeDOF = True).
*IA from your presentation should represent the entire rotor inertia; in the case of your hand calculation, you only used the hub inertia, HubIner.
Best regards,