Hooke`s Law


 * Hooke's law is a principle of physics that states that the force (F) needed to extend or compress a spring by some distance X scales linearly with respect to that distance. That is: F = kX, where k is spring constant, and X is the change of length which is small compared to the total possible deformation of the spring.


 * Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed limit of proportionality, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.

changing anymore. Let X be the amount by which the free end of the spring was displaced from its "relaxed" position (when it is not being stretched).
 * Suppose that the spring has reached a state of equilibrium, where its length is not


 * Hooke's law states that = kX where k is a positive real number, characteristic of the spring. Moreover, the same formula holds when the spring is compressed, with F and X both negative in that case. According to this formula, the graph of the applied force F as a function of the displacement X will be a straight line passing through the origin, whose slope is k.


 * Hooke's law for a spring is often stated under the convention that F is the restoring force exerted by the spring on whatever is pulling its free end. In that case, the equation becomes F = -kX, since the direction of the restoring force is opposite to that of the displacement.

some materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke's law is valid for it throughout its elastic range (i.e., for stresses below the yield strength). For some other materials, such as aluminium, Hooke's law is only valid for a portion of the elastic range.
 * Hooke's law only holds for