Solution to HW1

# Solution to HW1 - 0 1200 2.7>> A =.035.0001 10 2 0.02...

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Solution to HW1 EGM3344 Spring 2010 Problem 1.4 (b) The numerical solution can be implemented as The computation can be continued and the results summarized and plotted as: t v dv / dt 0 0 9.81 2 19.6200 6.2087 4 32.0374 3.9294 6 39.8962 2.4869 8 44.8700 1.5739 10 48.0179 0.9961 12 50.0102 0.6304 Note that the analytical solution is included on the plot for comparison

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1.8 The first two steps yield
2.2 >> z = linspace(-4,4); >> f = 1/sqrt(2*pi)*exp(-z.^2/2); >> plot(z,f) >> xlabel('z') >> ylabel('frequency') 2.3 (a) >> t = linspace(5,29,5) t = 5 11 17 23 29 ( b ) >> x = linspace(-3,4,8) x = -3 -2 -1 0 1 2 3 4 2.5 F = [11 12 15 9 12]; >> x = [0.013 0.020 0.009 0.010 0.012]; >> k = F./x k = 1.0e+003 * 0.8462 0.6000 1.6667 0.9000 1.0000 >> U = .5*k.*x.^2 U = 0.0715 0.1200 0.0675 0.0450 0.0720 >> max(U) ans =

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Unformatted text preview: 0. 1200 2.7 >> A = [.035 .0001 10 2; 0.02 0.0002 8 1; 0.015 0.001 19 1.5; 0.03 0.0008 24 3; 0.022 0.0003 15 2.5] A = 0.0350 0.0001 10.0000 2.0000 0.0200 0.0002 8.0000 1.0000 0.0150 0.0010 19.0000 1.5000 0.0300 0.0008 24.0000 3.0000 0.0220 0.0003 15.0000 2.5000 >> U = sqrt(A(:,2))./A(:,1).*(A(:,3).*A(:,4)./ (A(:,3)+2*A(:,4))).^(2/3) U = 0.3624 0.6094 2.5053 1.6900 1.1971 2.8 >> t = 10:10:60; >> c = [3.4 2.6 1.6 1.3 1.0 0.5]; >> tf = 0:75; >> cf = 4.84*exp(-0.034*tf); >> plot(t,c,'s',tf,cf 2.10 >> v = 10:10:80; >> F = [25 70 380 550 610 1220 830 1450]; >> vf = 0:90; >> Ff = 0.2741*vf.^1.9842; 2.14 (a) t = 0:pi/50:10*pi; subplot(2,1,1);plot(exp(-0.1*t).*sin(t),exp(-0.1*t).*cos(t)) title('(a)') subplot(2,1,2);plot3(exp(-0.1*t).*sin(t),exp(-0.1*t).*cos(t),t); title('(b)')...
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