PROBLEM 2 Identify the linear regression and nonlinear regression to fit the giv

Question

PROBLEM 2 Identify the linear regression and nonlinear regression to fit the given data for the following problem. Hooke's law, which holds when a spring is not stretched too far, signifies that the extension of the spring and the applied force are linearly related. The proportionality is parameterized by the spring constant k. A value for this parameter can be established experimentally by placing known weights onto the spring and measuring the resulting compression.Such data were plotted in the given figure. Notice that above a weight of 40 x 104 N, the linear relationship between the force and displacement breaks down. Use a inear regression to match the linear part and use a nonlinear regression to match the nonlinear portion. Then, use a piecewise function to represent both portions. Verify by plotting the function together with the data points and discussing results Displacement m010 017 027 035 039 042 043044 Force, 10'NO200 4050 70 80 Hooke's law Nonideal behavior: spring is hardening 0.2 Displacement, m 0.4

Explanation / Answer

For linear portion, The spring force kx should be equal to the total load. Therefore, the value of k can be determined in each point of observation. Since, solving the equation,

F=kx, for each F & x in the observed result, we can conclude that for linear part, after regression analysis, we can find that the regression line will be F=129.4278*104 x -3.13351.

For, the non linear portion, running the regression analysis,

we find that F=0.1432e14.384x.

For whole part of the data, after regression analysis,

we can use the exponential equation F=6.6394e5.4012x

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