Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component Fx = kx−bx^2+cx^3 must be applied to the free end. Here k=100N/m, b=700N/m^2, and c=12000N/m^3. Note that x>0 when the spring is stretched and x<0 when it is compressed. (Many real springs behave in a similar fashion.)
(a) How much work must be done to stretch this spring by 0.050 m from its unstretched length?
(b) How much work must be done to compress this spring by 0.050 m from its unstretched length?
(c) How much work must be done to move the spring from being compressed by 0.070 m to being stretched by 0.030 m, assuming the end moves with constant speed during the motion?