Question

I have the following data which reprent a free falling object. calculte the first derivative at each point and plot this data. use the attached defintion for the calculation

Also calculate the second derivative at each point using the formula and plot this the data.

use the attached defintion for the calculation

Do not use matlab predefined commands but the attachef definitions. Use h set to 0.1

Data:

(0,800) (3.9,732) (7.5,592) (13.9, 290) (20, 5)

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Answer 1

Below is the code for matlab for calculating the first and second-order derivatives using analytic expressions.

#code begins

h = 0.1; f = [800 732 592 290 5]; t = [0 3.9 7.5 13.9 20];

for i = 1:length(f) - 1
first_derivative(i) = (f(i+1) - f(i))/h; end;

for i = 2:length(f) - 1

second_derivative(i) = ( f(i+1) - (2*f(i)) + f(i) )/(h*h);

end;

#code ends

Both the expressions for the derivatives are second-order accurate as the higher-order terms are neglected.