A scale is made of two springs, as shown in the figure. The springs are nonlinear such that the force they apply is given by FS = K1u + K2u3, where the K's are constants and u = L - L0 is the elongation of the spring (L = ˆša2 + (b + x)2 and L0 - ˆša2 + b2 are the current and initial lengths of the springs, respectively). Initially, the springs are not stretched. When an object is attached to the ring, the springs stretch and the ring is displaced downward a distance x. The weight of the object can be expressed in terms of the distance x by:
W = 2FS (b + x)/L
For the given scale a = 0.22 m, b = 0.08m, and the springs' constants are K1 = 1600N/m and K2 = 100000N/m3. Plot W as a function of x for 0