Making a Cubic Spline (by-hand) Take just the last three points from the H(t) data above (re-printed at right), and develop a cubic-spline BY-HAND that matches that data, and use it to estimate the height at t 1.5 and t 2.5 seconds. For the two end points (t 1 and t-3) apply "natural spline" (" 0) conditions 1 7 When I say "by-hand" what I mean is (and show your work!!!) write out the form of the cubic interpolating polynomials, F(x)-a bxxdx3, in both intervals 1 and 2), apply all matching conditions to create a system of 8 equations with 8 unknowns, re-write these equations in matrix form (Ax-b), use MATLAB to solve for the 8 unknown coefficients, [OK to use MATLAB for just this step!] Finally, by-hand again, use the resulting functions to interpolate the force required at both t1.5 and t 2.5 Then feel free to compare the interpolated value at t-2.5 from the spline with the value you got with the cubic and linear polynomials in 7.1. What do you think is "best