Problem 2. (Module 7)

The measured velocity of a moving object is recorded in Table 2.

1. Find the natural cubic spline that passes through the points presented in Table 2. Suppose the equality of the first and the second derivatives for the internal points and the second derivative boundary conditions S(t₁) = 0, S(t₅) = 0
2. Use the cubic polynomials presentation in the form at3+bt2+ct+d .
3. Plot the entire data and spline polynomials.

Note: Matlab program Mod7_QuadraticPoly.m that used in Section 7.1.2 Module 7, as well as Matlab prog Mod7_Example1.m can be used. However, this program needs to be adapted to the data presented in Table 2. See also Section 7.1.3 of module #7 to form the corresponding matrix.

Time (t), s Velocity (v), ft/s 120 564 873 1012 1670 Time (t), s Velocity (v), ft/s 120 564 873 1012 1670