hwk09_soln - ! ! xmax occurs at t = T xmax = I = " /!...

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Unformatted text preview: ! ! xmax occurs at t = T xmax = I = " /! n # A sin! nt dt = 0 2A !n x = 0 occurs between T < t < 3T / 2 xmin occurs at t = 2T xmin = !2 I x = 0 occurs at t = 5T / 2 xmax occurs at t = 3T xmax = 2 I x = 0 occurs at t = 7T / 2 xmin occurs at t = 4T xmin = !2 I ! xmax occurs at t = T / 2 xmax = I = " /! n # A sin! nt dt = 0 2A !n x = 0 occurs at t = T xmin occurs at t = 3T / 2 xmin = ! I x = 0 occurs at t = 2T () x 0 = 0 for all t > 2T ! ! clear clc  %identity,mass,flexibilityandDmatrices I=eye(3)  M=eye(3)  A=[1/35/64/3 5/68/314/3 4/314/39]  D=A*M   %naturalfrequenciesandmodalvectors [Y,d]=eig(I,D)  [omega,id]=sort(sqrt(diag(d)))  Y=Y(:,id)   %forcingvector f=[0 1 0]   %normalizemodalvectors n=size(D,1)  alpha=sqrt(diag(Y'*D*Y))'  Y_norm=Y./[ones(n,1)*alpha]   %outputnaturalfrequenciesandnormalizedmodalvectors omega1=omega(1) Y1_norm=Y_norm(:,1) c1=Y1_norm'*A  y1=c1*f/omega1*Y1_norm omega2=omega(2) Y2_norm=Y_norm(:,2) c2=Y2_norm'*A  y2=c2*f/omega2*Y2_norm omega3=omega(3) Y3_norm=Y_norm(:,3) c3=Y3_norm'*A  y3=c3*f/omega3*Y3_norm    ...
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This document was uploaded on 12/23/2011.

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