Question

InClassHandout21 P1) A5 m long beam is loaded by a triangular distributed load. (a) It is known that the vertical deflection of the beam y is exactly given by a 5th degree polynomial in x, what is the minimum number of points at which the deflection should be measured precisely to obtain the 5th degree polynomial? (b) Obtain the interpolating polynomial for the data given below by solving a linear system (you may use MATLAB to invert the resulting matrix) Position x (m) 0 Deflection y (cm)0 5.76 8.82 -7.68 3.24 (c) What percentage of the error/uncertainty with respect to the mean (given by value) would you expect to be reduced by the interpolating polynomial obtained in (a)obtain the interpolating polynomial forthe data given in b) using Lagrange (e) Determine the deflection of the beam midway between the supports using the (f) Determine the deflection of the beam midway between the supports using the (g) At what positions is the deflection in the beam-7.5 cm? Solve using in-built (b)? interpolating polynomials (there is no need to simplify the resulting expression) results from (b) by hand results from (d) by hand functions in MATLAB. Note that there would be multiple positions and you need to get all of them. Submit screenshot of functions/commands. (h)What is the maximum deflection and at what position does it occur? You may use in- built MATLAB functions to solve for this Submit screenshot of functions/commands. (i) Plot the deflection in MATLAB as a smooth curve and confirm the results visually from (g) and (h). Submit a screenshot of the plot.

Answer 1

Please rate the answer. Thank you!

As per Chegg policy, kindly upload more than 4 questions separately. Thank you!

polunomia,twe require nt'points eg ree polynomialoe require '6'points se MATLAB to get polynomi ol.. [code is o- 5.76- 8. 82 -7.68-3.24-+O 6 5 8.82 68 S Stot 2 de Logranges polyno Co-מ) 0-2 () 0-3) CO-4) (0-5) C-4) CI-5) cx-O)(2-1)(2-2 C3-o)C3-D (3-2 C2-0 C2-C2-3) C2-4 (2-5 C3-4) C3-5) (1-3)(7-5) (4-3) C4-5 C-320 t

1 x-[0 1 234 5]; 2 y [0 -5.76 -8.82 -7.68 -3.24 01; 3 polyfit(x,y,5) ans -1.0000e-02 5.5233e-15 5.0000e-01 -6.5727e-14 6.2500e+00 -1.7455e-14