Approximating and regression method

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Hi guys,

I did a few sets of test in determining the natural frequency of a crane lifting loads. From that, I tried to find two constant from its initial function.

upload_2016-4-5_20-30-10.png


a is the stiffness of the pole that was holding the crane
b is the weight of the crane
x is the weight of the load

The tests were completed by using three different loads on three different position. I plotted the graph as below.

upload_2016-4-5_20-36-7.png


From the obtained graph and the initial function, I tried to determine the value of constant A and B. By calculating manually, the value of A and B are not constant but it supposed to be constant. I tried using MATHCAD to find the value of the constants by using nonlinear regression method but I am not convince that is a right solution. Any of you know any mathematical approximation method that I can use?
 

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Svein
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Any of you know any mathematical approximation method that I can use?
Excel does linear regression directly. If you want it mathematically, you must calculate:
  1. [itex]s_{1}=\sum x_{j} [/itex]
  2. [itex]s_{2}=\sum x_{j}^{2} [/itex]
  3. [itex]t_{1}=\sum y_{j} [/itex]
  4. [itex]t_{2}=\sum y_{j}^{2}[/itex]
  5. [itex]v_{1}=\sum x_{j}\cdot y_{j} [/itex]
Assuming that you have n points, you then calculate [itex]a=\frac{t_{1}\cdot s_{2}-s_{1}\cdot v_{1}}{n\cdot s_{2}-s_{1}^{2}} [/itex] and [itex] b=\frac{n\cdot v_{1}-s_{1}\cdot t_{1}}{n\cdot s_{2}-s_{1}^{2}}[/itex]. The regression line is then given by [itex] y=a\cdot x + b[/itex].
 

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