A DC motor is given ac to vibrate ta different frequencies and a bode plot of gain and phase are plotted. I need to understand why the motor is not following a sine profile at low frequencies when connected to a tacho. The reason I can imagine is the inertia of the armature and flywheel creates some hysteresis. Is this correct?

 

Is your motor a reversible brushless DC design? There is a bias in the way the brushes are held in a brushed DC motor that can make reverse movement slower.

http://en.wikipedia.org/wiki/Brushed_DC_electric_motor

http://www.mabuchi-motor.co.jp/en_US/product/p_0305.html