When a rubber is stretched during a tensile test, its elongation is initially proportional to the applied force, but as it reaches about twice its original length, the force required to stretch the rubber increases rapidly. The force, as a function of elongation, that was required to stretch a rubber specimen that was initially 3cm long.

(a) Curve-fit the data with a forth order polynomial. Make a plot of the data points and the polynomial. Use the polynomial to estimate the force when the rubber specimen was 11.5cm long.
(b) Fit the data with spline interpolation (use MATLAB built-in function interp1). Make a plot that shows the data points and a curve made by interpolation. Use interpolation to estimate the force when the rubber specimen was 11.5cm long

Table 1

Elongation vs. force for rubber during tensile test.

Elongation (cm) Force (KN)
0 0
1.2 0.6
2.4 0.9
3.6 1.16
4.8 1.18
6.0 1.19
7.2 1.24
8.4 1.48
9.6 1.92
10.8 3.12
12.0 4.14
13.2 5.34
14.4 6.22
15.6 7.12
16.8 7.86
18.0 8.42