Discuss the force - displacement graph for a spring.

Explanation

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