Please answer only Question #4 and write a MatLab code. Thank you.

1. A bar with uniform cross-sectional area A, elastic modulus E, and length L is loaded with distributed loads q(r). The bar is fixed on the left end and attach to the spring of stiffness which is relaxed when the bar is undeformed A as .02, the Young's modulus E as 210 GPa (Steel ASTM A36), K = 1 000kN/m Spring constant K F(spring) Cross sectional Area: A(m2) L (m) d2u(x) B. C: u(0) = 0, F =-Ku(L) (2x)2 q0-12- x = [0, ] q (x) = do (40 points) Write a MATLAB program which Takes as input: Length of the bar, number of intervals N and q0 Assembles the FD matrices Run your program using length L-5 (unit: m), qo-5 (unit: KN), and when N=2,4,8 and N=16 2. (10 points) Find the exact solution to the problem, then plot the exact solution with FD solutions for N=2, 4, 8 and N-16 on the same plot