▁( A ▁+ ▁B ) ▁produces ▁response ▁( X ▁+ ▁Y ). ▁ ▁A ▁function ▁ ▁that ▁satisfies ▁the ▁super position ▁principle ▁is ▁called ▁a ▁linear ▁function . ▁Super position ▁can ▁be ▁defined ▁by ▁two ▁simpler ▁properties ; ▁add itivity ▁and ▁hom ogene ity ▁▁ ▁Add itivity ▁ ▁Hom ogene ity ▁ ▁for ▁scalar ▁. ▁ ▁This ▁principle ▁has ▁many ▁applications ▁in ▁physics ▁and ▁engineering ▁because ▁many ▁physical ▁systems ▁can ▁be ▁mode led ▁as ▁linear ▁systems . ▁For ▁example , ▁a ▁beam ▁can ▁be ▁mode led ▁as ▁a ▁linear ▁system ▁where ▁the ▁input ▁stim ulus ▁is ▁the ▁load ▁on ▁the ▁beam ▁and ▁the ▁output ▁response ▁is ▁the ▁def lection ▁of ▁the ▁beam . ▁The ▁importance ▁of ▁linear ▁systems ▁is ▁that ▁they ▁are ▁easier ▁to ▁analyze ▁mathemat ically ; ▁there ▁is ▁a ▁large ▁body ▁of ▁mathematical ▁techniques , ▁frequency ▁domain ▁linear ▁transform ▁methods ▁such ▁as ▁Fourier , ▁Lap lace ▁transform s , ▁and ▁linear ▁operator ▁theory , ▁that ▁are ▁applicable . ▁Because ▁physical ▁systems ▁are ▁generally ▁only ▁approximately ▁linear , ▁the ▁super position ▁principle ▁is ▁only ▁an ▁approximation ▁of ▁the ▁true ▁physical ▁behaviour . ▁ ▁The ▁super position ▁principle ▁applies ▁to ▁any ▁linear ▁system , ▁including ▁algebraic ▁equations , ▁linear ▁differential ▁equations , ▁and ▁systems ▁of ▁equations ▁of ▁those ▁forms . ▁The ▁stim uli ▁and ▁responses ▁could ▁be ▁numbers , ▁functions , ▁vectors , ▁vector ▁fields , ▁time - v ary ing ▁signals , ▁or ▁any ▁other ▁object ▁that ▁satisfies ▁certain ▁ax i oms . ▁Note ▁that ▁when ▁vectors ▁or ▁vector ▁fields ▁are ▁involved