Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

Engineering 25 Problems1.[23, 26] Solutions Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

P1.23 FT approximation • Consider the Step Function • The Fourier Transform for the above Function • Taking the First FOUR Terms of the Infinite Sum

P.1-23 FT m-file & plot % Bruce Mayer, PE % EGNR25 * 23Jun11 % file = ENGR-25_Chp1_Tutorial_fft-n-Law-of-Cos_110829.pptx% % delx = 1e-6 % for small increment on either side of ZERO % % Make STEP-function plotting vector x1 = [-pi,0-delx, 0+delx, pi] f1 = [-1,-1,1,1] % % Make FFT plotting vectors x2 =-pi:0.01:pi; f2 = (4/pi)*(sin(x2)/1 + sin(3*x2)/3 + sin(5*x2)/5 + sin(7*x2)/7); % % Plot Both with a grid plot(x1,f1, x2,f2, 'linewidth',3), grid

P1-26 Law of CoSines • Given Irregular Quadrilateral • By Law of CoSines

P1-26 Law of CoSines • Given Quantities  • Find c2 when • Instructor to WhtBd to Build Quadratic Eqn in c2

P1-26 Law of CoSines • Build Quadratic Eqn in c2 • Instructor to Write m-file from Scratch (start w/ blank m-file)

P1-26 mFile & Results % Bruce Mayer, PE % EGNR25 * 23Jun11 % file = P1_26_LawOfCos_1106.m % % % Set Known ParaMeters b1 = 180; b2 = 165; c1 = 115; % all in meters A1 = 120; A2 = 100; % all in Degrees % % Calc the constant a^2 asq = b1^2 + c1^2 -2*b1*c1*cosd(A1) % note use of cosd % % Make Quadratic PolyNomial c2Poly = [1, -2*b2*cosd(A2), (b2^2 - asq)] % % Find roots of PolyNomial c2roots = roots(c2Poly) % % NOTE: since c2 is a DISTANCE it MUST be POSITIVE sq = 66325 c2Poly = 1.0e+004 * 0.0001 0.0057 -3.9100 c2roots = -228.4542 171.1503 ANSWER

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege