Using numerical differentiation to compute moment

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Lingbai Ren
Lingbai Ren on 15 Sep 2021
Commented: Walter Roberson on 15 Sep 2021
I have the measurements of x with corresponding y displacement lengths:
x = [0,0.375,0.75,1.125,1.5,1.875,2.25,2.625,3];
y = [0,-0.2571,-0.9484,-1.9689,-3.2262,-4.6414,-6.1503,-7.7051,-9.275];
and dy/dx = theta(x) (1) >> theta is the slope
d-theta/dx = d^2y/dx^2 = M(x)/EI (2) >> M(x) is the bending moment
x is the diatance along the beam
y is the displacement
E is the modulus of elasticity (E = 200)
I is the moment of Inertia (I = 0.0003)
I am wondering how to use the following 2 approaches to compute Moment M(x)
(a)Numerically differtiate the first derivative of the theta(x) approximations from the previous part (which is the question I asked before)
then
(b)Numerically differentiate the second derivative of the measured y(x) data provided.
I guess my question would be how to differentiate a vector of numbers? Is there a numerical method we can apply in this case?

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