Mathematical models of physical phenomena are infinitely precise. However, we are not able to make measurements of physical phenomena with anywhere near that precision. Therefore, we often must fit the data we measure to a mathematical model we construct to describe the system. How well the data "fits" helps us understand how good our model is and how well our data collection systems perform.

Using the velocity and position data for a falling object provided by the instructor, do the following in MATLAB:

1) Add in instrumentation noise by introducing a random offset of your design. Explain the rationale for your range of values.

2) Fit the data to polynomial curves using the methods shown in the textbook.

3) Determine which "order" of curve best fits the data. The order refers to the highest power of the polynomial equation.

4) For both velocity and position, plot the curve and the data on the same figure.

Velocity: [11 31 64 112 176 259 362]

Position: [2 3 4 5 6 7 8]

Must use MatLab for this assignment.

Please type and display output for code and graph.

Thank you