Problem) In this problem, you will solve the same Problem I in Assignment 1, using different methods: Consider a simply supported beam as shown below. The beam is loaded with a distributed load. The deflection, y, of the centerline of the beam as a function of the position, x, is given by the following equations: w y=- (Lx+ - 2a(2L - a)x3 + a2 (2L - a)?x) for ( Sxsa 24EIL wa? 24EIL (L - x)(-2x + 4Lx - a?) for a Sxsl where L4 m is the length of the beam, E = 70 GPa is the elastic modulus, I=52.9x10^m^ is the moment of inertia, and w= 20 kN/m. Consider the case of a = 2L/3. You are asked to find the position, x, at which the deflection of the beam is maximum and the deflection at that point using the following methods: (Hint: the maximum deflection will occur between r= 0 and a, at a point where = 0) B) Write a MATLAB function that implements the Newton's method to solve f(x) =0, with following inputs and outputs: Inputs: initial guess, maximum iterations, tolerance, and the name (string) of the m-file that returns f(x). Output: root of equation f(x)=0 obtained using Newton's method. Use your completed code to solve the problem and report the position, x, at which the deflection of the beam is maximum and the deflection at that point. Also include your code in your submission. C) Use your function from Part B to obtain the convergence plot. That is, plot the estimated relative error *1*1-* | versus the iteration number. In this case, use tolerance E = 10-14 X X D) Compare the number of iterations necessary to achieve an estimated relative error 1*1*1** | SE smaller than le-9 (8) using Newton-Raphson Method and a tolerance in solution 1058 smaller than le-6 (8) using the Bisection Method. Report the solution (Xns, f (xns)) in each case. Which method requires fewer number of iterations? Submit all lines of code you have written for this part along with the results. E) Use MATLAB's built-in fzero function and obtain position, x, at which the deflection of the beam is maximum and the deflection at that point. Submit all lines of code you have written for this part along with the output. Problem) In this problem, you will solve the same Problem I in Assignment 1, using different methods: Consider a simply supported beam as shown below. The beam is loaded with a distributed load. The deflection, y, of the centerline of the beam as a function of the position, x, is given by the following equations: w y=- (Lx+ - 2a(2L - a)x3 + a2 (2L - a)?x) for ( Sxsa 24EIL wa? 24EIL (L - x)(-2x + 4Lx - a?) for a Sxsl where L4 m is the length of the beam, E = 70 GPa is the elastic modulus, I=52.9x10^m^ is the moment of inertia, and w= 20 kN/m. Consider the case of a = 2L/3. You are asked to find the position, x, at which the deflection of the beam is maximum and the deflection at that point using the following methods: (Hint: the maximum deflection will occur between r= 0 and a, at a point where = 0) B) Write a MATLAB function that implements the Newton's method to solve f(x) =0, with following inputs and outputs: Inputs: initial guess, maximum iterations, tolerance, and the name (string) of the m-file that returns f(x). Output: root of equation f(x)=0 obtained using Newton's method. Use your completed code to solve the problem and report the position, x, at which the deflection of the beam is maximum and the deflection at that point. Also include your code in your submission. C) Use your function from Part B to obtain the convergence plot. That is, plot the estimated relative error *1*1-* | versus the iteration number. In this case, use tolerance E = 10-14 X X D) Compare the number of iterations necessary to achieve an estimated relative error 1*1*1** | SE smaller than le-9 (8) using Newton-Raphson Method and a tolerance in solution 1058 smaller than le-6 (8) using the Bisection Method. Report the solution (Xns, f (xns)) in each case. Which method requires fewer number of iterations? Submit all lines of code you have written for this part along with the results. E) Use MATLAB's built-in fzero function and obtain position, x, at which the deflection of the beam is maximum and the deflection at that point. Submit all lines of code you have written for this part along with the output