Optional Homework Assignment: Solving beam differential equation in the reversed coordinate system – Fusion of Engineering, Control, Coding, Machine Learning, and Science

Consider the cantilever beam shown in Fig. 1 below.

Note the location of the coordinate system center. Assume that length $L$ , force $F$ , modulus of elasticity $E$ , and moment of inertia $I$ are given.

a) Derive the equations of deformation $y=y(F,L,E,I,x)$ .
b) For a chosen (realistic) values of $F$ , $L$ , $E$ , and $I$ , plot the function $y$ in MATLAB or in any other software that you know (Python, Mathematica).

Deadline: Friday, November 05, 2021, at 10:10 AM

IMPORTANT COMMENTS:

– Number of points: 5 points on the final exam (however, both a) and b) have to be completed successfully).

– During the lectures on Friday, we explained how to solve the bending differential equation to compute the deformation in the $y$ direction as a function of $x$ . However, the coordinate system center was different from the coordinate center location in Fig. 1. Consequently, the mathematical forms of equations will be different for two coordinate system locations.

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