Work Done on a Spring:

If a tensile force (F) is applied on a spring, it elongates through a distance (s) and the relation of (F) against (s) gives a straight line graph as shown in Figure. It is called as linear characteristic of the spring.

Consider F₁ be the force required to cause displacement (s₁) of the spring.

Consider F₂ be the force required to cause displacement (s₂) of the spring. Area under the curve gives work done by the force.

 (i)        W. D. on the spring to elongate it through a distance (s₁ ) = Δ O s₁  F₁

                                                 = F₁ s₁ / 2

 (ii)       W. D. on spring to elongate it a distance (s2 ) =  F₁ s₁ / 2

 (iii)      W. D. on spring through distance from s₁ to s₂ is given by

 = ((F₁ + F₂ )/2 ) (s₂ - s₁ ) the area of trapezium = ( F₁  F₂ s ₁ s₂  ) .

Furthermore, the force and deformation of a spring are associated by stiffness of the spring k, defined as the force required deforming it by a unit length.