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Non-Real Eigenvalues

  1. Nov 13, 2012 #1
    1. The problem statement, all variables and given/known data
    et0re.jpg



    3. The attempt at a solution
    I know the general form should be

    x1(t)=-C1sin(3t) + C2cos(3t)
    x2(t)=C1sin(3t) + C2cos(3t)

    but there's something going on with v that I'm not getting. I'm not sure how to incorporate it without knowing A
     
  2. jcsd
  3. Nov 13, 2012 #2

    Mark44

    Staff: Mentor

    The constants shouldn't be the same in both functions.
     
  4. Nov 13, 2012 #3
    Whoops, I wrote that wrong. All of the problems I have worked so far have had the form:


    x1(t)=-C1sin(3t) + C1cos(3t)
    x2(t)=C2sin(3t) + C2cos(3t)
     
  5. Nov 13, 2012 #4
    After looking through some more examples, the answer will have the form


    x1(t)=-C1sin(3t)*a + C1cos(3t)*b
    x2(t)=C2sin(3t)*a + C2cos(3t)*b

    where v=a+ib

    v = [-1-i,1] = [-1,1]+i[-1,0]

    a=[-1,1]
    b=[-1,0]

    I get:
    C1sin(3t)
    -C2cos(3t)

    But it's telling me that's incorrect.
     
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