Q$2$: Finite Difference Method

You have measured the following displacements along the length of a cantilevered beam with a linearly

increasing load.

The slope, $,$ of the beam is the first derivative of the displacement with respect to $x,$ as follows:

$\frac{dy}{dx}=(x)$

The first derivative of the slope, $,$ with respect to $x$ is related to the bending moment, $M(x),$ as follows:

$\frac{d}{dx}=\frac{d^{2}y}{d{x}^2}=\frac{M(x)}{EI}$

where $x$ is the distance along the beam, $y$ is the displacement, $E$ is the modulus of elasticity, and I is

the moment of inertia. Use the following physical parameters:

$E=200[GPa]$

$I=0\mathrm{.}0003[m^4]$

Write a Matlab or Python code to complete the following:

$(1$ pt$)$ Numerically differentiate the provided data for displacement, $y(x),$ to produce a table of

the slope, $(x),$ data. You can choose formulas of any error order.

$(2$ pts$)$ Use numerical differentiation to compute the moment, $M(x),$ using the following $2$

approaches $[$reference Eqn. $2]$:

$($a$)$ Numerically differentiate the first derivative of the $(x)$ a pproximations obtained in the

first part.

$($b$)$ Numerically differentiate the second derivative of the measured $y(x)$ data provided.

$(2$ pts$)$ Plot the moment, $M(x),$ obtained using each of the methods from the previous part.

Provide a comment regarding which method is more accurate and why. WRITE THE CODE IN MATLAB