I need help solving this question using Newtons Method and p

I need help solving this question using Newton\'s Method. and please make sure to include the Matlab code. Thank you

Solution

in order to compress or stretch a spring you have to do work. you must exert a force on the spring equal in magnitude to the force the spring exerts on you, but opposite in dirrection. the force you exert is in the direction of the displacement. you therefour do work. the average force you exert as you change the displacement from 0 to x is (1/2)kx. the work you do when stretching or stretching or compressing a spring therefore is

W=forece*distance=(1/2)kx*x=(1/2)kx2

as you do work, you transfer energy to the spring. the elastic potential energy stored in the spring is U=(1/20kx2