Problem 1: Matlab Three masses are attached to spring, k1 = 30 N/m, k2 = 25N/m, k3 = 20N/m, and k4 = 15N/m, as shown. Initially the masses are positioned such that the springs are in their natural length (not stretched or compressed); then the masses are slowly released and move downward to an equilibrium position as shown on the right. The equilibrium equations of the three masses are
where u1, u2, and u3 are the relative displacement (from the unstretched position) of each mass as shown.
If the masses have true weights W1 = 20N, W2 = 30N, and W3 = 15N. However, due to a bias error in the measuring device, the actual weight column vector on the right hand size used to determine the displacements is
where c is a constant representing the bias error in the weight measurements.
The effect of bias c on the error in the displacements u is studied by the error analysis equation
Write a Matlab script to complete the following tasks:
(a) Determine the true displacements using the true weights W1 , W2 , and W3 .
(b) Assume the bias c changes from 0 to 5 N with a step size of 0.1 N. For each value of c, determine (1) the lower error bound
(2) the upper error bound 
and (3) the relative error 
.
(c) Plot the lower bound vs. c, upper error bound vs. c, and relative error vs. c on the same graph (i.e., three curves in one figure).
Note: Please use 1-norm for the analysis and you may use the built-in function norm for this purpose.