MATLAB

The following differential equation results from a force balance for a beam with a uniform loading, 0= EI dx 2 where x-distance along the beam (m), y = deflection (m), L = length (m), E= modulus of elasticity (N/m2), moment of inertia (m4), and w= uniform load (N/m). (a) Convert this differential equation to an equivalent system of simultaneous algebraic equations using a centereddifference approximation for the second derivative. (b) Develop a function to soive these equations from x s0 to Land return the resulting distances and deflections. The first line of your function should be function [x, y] = YourLastName, beam (E, I, w, yo, yL, L, dx) (c) Develop a script that invokes this function and then plots the results. (d) Test your script for the following parameters: L = 3 m, : 0.2 m, E-250 x 109 N/m2, 10-4 m4, w= 22,500 Nm, y(0) = 0, and y(3) = 0. 3 x The following differential equation results from a force balance for a beam with a uniform loading, 0= EI dx 2 where x-distance along the beam (m), y = deflection (m), L = length (m), E= modulus of elasticity (N/m2), moment of inertia (m4), and w= uniform load (N/m). (a) Convert this differential equation to an equivalent system of simultaneous algebraic equations using a centereddifference approximation for the second derivative. (b) Develop a function to soive these equations from x s0 to Land return the resulting distances and deflections. The first line of your function should be function [x, y] = YourLastName, beam (E, I, w, yo, yL, L, dx) (c) Develop a script that invokes this function and then plots the results. (d) Test your script for the following parameters: L = 3 m, : 0.2 m, E-250 x 109 N/m2, 10-4 m4, w= 22,500 Nm, y(0) = 0, and y(3) = 0. 3 x