PLEASE USE MATLABProblem 1a: Finite Difference Method for Boundary Value Problem A proposed design of a column of length L = 10m will be hinged at its top and bottom and loaded by a compressive vertical force P = 1 kN which is offset from the columns axis by a distance e = 0.05m. The column can buckle under the compressive load, exhibiting a horizontal displacement y = y(x) as shown in the figure. Here 0 ? x ? L locates points on the column from the bottom. The columns aluminum material has Youngs modulus E = 71 GPa and moment of inertia I = bh3/12 dependent on the columns cross sectional dimensions b = 0.05m and h = 0.05m. Static equilibrium of the column has the horizontal displacement governed by the Boundary Value Problem consisting of the differential equation and boundary conditions Generate a numerical solution for the buckled displacement profile y = y(x) using finite differences with step size h = 0.1 m, then plot y = y(x). Estimate the value of the slope y(0) at x = 0 from your solution, and denote this as yp0.

Problem 1a: Finite Difference Metho t Boundary Value Problem design of a column of length L 10m will be hinged at its top and bottom and loaded by a compressive vertical force P 1 kN which is offset from the column's axis by a distance e-0.0m. The column can buckle under the compressive load, exhibiting a horizontal displacement (x) as shown in the figure Here 0 s s ? locates points on the column from the bottom. The column's aluminum material has Young's modulus E 71 GPa and moment of inertia l-br112 dependent on the column's cross sectional dimensions b 005m and h- 0.05m Static equilibrium of the column has the honizontal displacement governed by the Boundary Value Problem consisting of the differential equation and boundary conditions Dispiaced y(00 nerate a aumericat solution Toi the buc kied displacemsat profie y eeusing tinite O fiom your soltution and denote this as differences with step ize dd01 m. then plot y (n Estimate the roblem lb: Shooting Method for Bou nda Problem Here vou will ner er nun tion to the Ple Problem 1a: Finite Difference Metho t Boundary Value Problem design of a column of length L 10m will be hinged at its top and bottom and loaded by a compressive vertical force P 1 kN which is offset from the column's axis by a distance e-0.0m. The column can buckle under the compressive load, exhibiting a horizontal displacement (x) as shown in the figure Here 0 s s ? locates points on the column from the bottom. The column's aluminum material has Young's modulus E 71 GPa and moment of inertia l-br112 dependent on the column's cross sectional dimensions b 005m and h- 0.05m Static equilibrium of the column has the honizontal displacement governed by the Boundary Value Problem consisting of the differential equation and boundary conditions Dispiaced y(00 nerate a aumericat solution Toi the buc kied displacemsat profie y eeusing tinite O fiom your soltution and denote this as differences with step ize dd01 m. then plot y (n Estimate the roblem lb: Shooting Method for Bou nda Problem Here vou will ner er nun tion to the Ple