Discuss the force - displacement graph for a spring.

Explanation

The restoring spring force and displacement are linearly related as `F=-kx`. They are opposite in direction. Hence, the graph between F and x is a straight line with dwelling only in the second and fourth quadrant as shown in the figure. The elastic potential energy can be calculated by drawing a F - x graph. The shaded area (triangle) is the work done by the spring force.
Area = `(1)/(2)` (base) (height)
`=(1)/(2)xx(x)xx(kx)=(1)/(2)kx^(2)`