its the third level order using derivatives. I'm really drawing a blank on this problem.. because this has to be entered through MAple soft its very confusing. Each problem is taking more than 5 hours to solve. nd I don't know how to approach this one. If you can help me get started in the right direction with the formula input it would highly appreciated
A "cubic spline" is a piecewise cubic function. A "clamped" cubic spline has both values and derivatives given at the endpoints. Here were are given the values (distance) and derivative (speed) at every point.
Any cubic can be written in the form $\displaystyle f_0(t)= a_0t^3+ b_0t^2+ c_0t+ d_0$. At the first point, t= 0, we are given $\displaystyle f_0(0)= d_0= 0$ and $\displaystyle f'(0)= c_0= 75$. At the second point, t= 3, we are given $\displaystyle f_0(3)= 27a_0+ 9b_0+ 3c_0+ d_0= 225$ and $\displaystyle f_0'(3)= 27a_0+ 6b_0+ c_0= 77$. We have four equations to solve for the four coefficients.
Between t= 3 and t= 5 we may have a different cubic which we can write as $\displaystyle f_1(t)= a_1t^3+ b_1t^2+ c_1t+ d_1$. At t= 3, we have $\displaystyle f_1(3)=27a_1+ 9b_1+ 3c_1+ d_1= 225$ and $\displaystyle f_1'(3)= 27a_1+ 6b_1+ c_1= f_1'(3)= 77$. At t= 5 we have $\displaystyle f_1(5)= 125a_1+ 25b_1+ 5c_1+ d_1= 383$ and $\displaystyle f_1'(5)= 75a_1+ 10b_1+ c_1= 83$, again four equations to solve for the four coefficients.
Continue that over the intervals from t= 5 to 8 and from t= 8 to 13.