Determine the true displacements using the true weights

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Reference no: EM131067664

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

2137_martix.png

1684_M.png

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

213_matrix1.png

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

2120_matrix2.png

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

1953_matrix3.png (2) the upper error bound 2232_matrix4.png and (3) the relative error 1707_matrix5.png.

(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.

Reference no: EM131067664

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