t ) ▁= ▁( x ( t ), ▁y ( t ), ▁z ( t )), ▁is ▁calculated ▁using ▁its ▁velocity , ▁v ▁= ▁( v x , ▁vy , ▁v z ), ▁to ▁obtain ▁ ▁For ▁convenience , ▁consider ▁contact ▁with ▁the ▁spring ▁occurs ▁at ▁t ▁= ▁ 0 , ▁then ▁the ▁integral ▁of ▁the ▁product ▁of ▁the ▁distance ▁x ▁and ▁the ▁x - vel ocity , ▁x v x , ▁is ▁x 2 / 2 . ▁ ▁The ▁function ▁▁ ▁is ▁called ▁the ▁potential ▁energy ▁of ▁a ▁linear ▁spring . ▁ ▁El astic ▁potential ▁energy ▁is ▁the ▁potential ▁energy ▁of ▁an ▁el astic ▁object ▁( for ▁example ▁a ▁bow ▁or ▁a ▁cat ap ult ) ▁that ▁is ▁de formed ▁under ▁t ension ▁or ▁compression ▁( or ▁str essed ▁in ▁formal ▁termin ology ). ▁It ▁ar ises ▁as ▁a ▁consequence ▁of ▁a ▁force ▁that ▁tries ▁to ▁restore ▁the ▁object ▁to ▁its ▁original ▁shape , ▁which ▁is ▁most ▁often ▁the ▁elect romagnet ic ▁force ▁between ▁the ▁atoms ▁and ▁mole cules ▁that ▁const itute ▁the ▁object . ▁If ▁the ▁stretch ▁is ▁released , ▁the ▁energy ▁is ▁transformed ▁into ▁kin etic ▁energy . ▁ ▁Pot ential ▁energy ▁for ▁gravit ational ▁forces ▁between ▁two ▁bodies ▁ ▁The ▁gravit ational ▁potential ▁function , ▁also ▁known ▁as ▁gravit ational ▁potential ▁energy , ▁is : ▁ ▁The ▁negative ▁sign ▁follows ▁the ▁convention ▁that ▁work ▁is ▁gained ▁from ▁a ▁loss ▁of ▁potential ▁energy . ▁ ▁Der iv ation ▁▁ ▁The ▁gravit ational ▁force ▁between ▁two ▁bodies ▁of ▁mass ▁M ▁and