Re: why does brown sugar relieve the pain caused by period?

Menstrual cramps are caused by contraction of the smooth muscles of the 
uterus.  These muscle contractions are modulated by prostaglandins, which 
are derivatives of the fatty acid, arachidonic acid.  This type of fatty 
acid is one of the "omega-3" fatty acids and is found primarily in marine 
animals.  Brown sugar does not contain arachidonic acid and has no 
influence on smooth muscle contractions.  Any effect on menstrual cramps 
would be psychological rather than physiological.

Reference:  Shils, Olson, and Shike.  Modern Nutrition in Health and 
Disease.  Eighth edition.