d^w Consider a beam that can be described by Euler-Bernoulli Beam ODE EI q(x). Assume the beam 10 meters long, has an area moment of inertial of 8e-5 m, has one fixed-end boundary condition (w' = 0 and w= 0), and one pinned-end boundary condition (w" = 0 and w = 0). If we make measurements of the displacement as illustrated in the HW4_P1.png file, what is the beam made of? Assume a constant load of -10kN/m on top of the beam. Deliverables (Submit the code electronically as LastName_Problem1.m ad as a PDF file publication) . . = . Code implementation in MATLAB opens the image file and allows you to manually pick and build the displacement profile of the beam, then use the displacement profile to compare with the beam solution for a range of appropriate materials. A comment at the end of the MATLAB code identifies the material based on elastic modulus and know (you can find a list of material properties at: https://www.engineeringtoolbox.com/young-modulus-d_417.html). Problem 2 [50 pts] Consider a 4-way intersection from a square ventilation duct (Edge Length = 0.25 meters) that is transporting hot air at a steady temperature. The outside of the duct is at room temperature (20 C), and there are two inlets (one at 25C and one at 30C) and two outlets (both at 27.5C). Using the Poisson Equation for temperature distribution with no heat transfer at the center plane 8T 87 + = 0) discuss what the temperature distribution would look like if the x ay of the duct outlets were across from each other in contrast to next to each other. Assume the temperature gradually changes from the edge temperature (20 C) to the constant duct temperature with 0.025 meters from each edge. Deliverables (Submit the code electronically as LastName_Problem2.m and as a PDF file publication) Problem formulation in MATLAB comparing both solutions A short discussion at the end of the MATLAB code commented out