University of Florida/Eml4507/s13.team3.DavidPatrickR4

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Problem 4.1[edit]

On my honor, I have neither given nor received unauthorized aid in doing this assignment. 

Given[edit]

Mode Shape for system. Mode slope increases and crosses into the positive region

Spring-damper-body arrangement as shown. Two separate forces applied to masses.
















γ γ





Find[edit]

Find the eigenvector corresponding to the eigenvalue for the spring-mass-damper system on p.53-113. Plot and comment on this mode shape. Verify that the eigenvectors are orthogonal to each other

Solution[edit]

Eigenvalues are found



We find the eigenvectors from







Set








Eigenvectors are orthogonal to each other:

EDU>> x= [-.8507;-.5257];
EDU>> y= [-.5257;.8507];
EDU>> transpose(y)*x
ans = 0

Problem 4.2[edit]

 On my honor, I have neither given nor received unauthorized aid in doing this assignment. 

Given[edit]

Use same given values as in problem 4.1

Find[edit]

Mode Shape for system. Notice plot is the same even with different initial conditions

Find the eigenvectors for and when setting


Solution[edit]

We find the eigenvectors from







Set











We find the eigenvectors from







Set