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March 30, 2017

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-From the following two linear homogeneous algebraic equations:(sqr= square root)

(1) B*sin(kl/sqr2) = D*sin(kl)
(2) (k/sqr2)*B*cos(kl/sqr2) = (k)*D*cos(kl)

-Form matrix of these 2 equations and solving the determinant=0 will lead to: (1/sqr2)*cos(kl/sqr2)*sin(kl) - sin(kl/sqr2)*cos(kl)= 0

-How do i solve this?

  • Engineering - ,

    I do not see why the determinant must be zero. Your final equation is a statement that it IS zero, except you seem to have left out an "l" term after the first k in equation 2.

    You final equation is of the form
    a*cosA*sinB -sinA*cosB = 0
    a = tanA/tanB
    where a = 1/sqrt2
    A = k*l/sqrt2
    B = k*l
    You may have to solve for kl by iteration. I don't see an easy way.

  • Engineering - ,

    If it's of any help, here's a plot of the function
    f(x)=sqrt(2)*cos(x)*sin((x)/sqrt(2))-sin(x)*cos((x)/sqrt(2))

    http://imageshack.us/photo/my-images/196/1319958400.png/

    Since there is only one variable, and the graph is harmonic, there's probably a way to solve the equation, but I cannot think of one for now. Use iteration as drwls suggested for the moment.

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