I am trying to conduct an experiment to verify the potential energy of a spring is equal to 1/2kx^2. Using hooke's law I have plotted a graph of Force (mass*gravity) versus spring extension. The slope of the line of best fit has given me the the spring constant (k). Since Work is the integral of Force and distance, measuring the area under the graph would give: 1/2F*x (using the formula for area of a triangle) where F=kx, thus 1/2(kx)*x which equals 1/2kx^2. Since work done on a spring is equal to the potential energy stored in the spring, would this be sufficient to verify the equation? Or is there an additional part of the experiment that I should include?

Force (N) 1.4 Force vs Extension 1.2 0.8 0.6 0.4 0.2 1 y= 24.989x+0.0357, 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Extension (m)