 The work of this spring on a body moving along the space curve s("t") = ("x"("t"), "y"("t"), "z"("t")), is calculated using its velocity, v = ("v"x, "v"y, "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"-velocity, "xvx", is "x"2/2.The function 
is called the potential energy of a linear spring.Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology).