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Find the response to the input

  1. Oct 4, 2007 #1
    1. The problem statement, all variables and given/known data
    for an LTIC system described by the transfer function
    [tex]H(s)=\frac{s+2}{s^2+5s+4}[/tex]

    find the response to the following everlasting sinusoidal inputs:
    5*cos(2t+30 degrees)


    3. The attempt at a solution
    [tex]H(jw) = \frac{jw+2}{4-w^2+j5w}[/tex]

    [tex]|H(jw)|=\sqrt{\frac{w^2+4}{(4-w^2)^2+25w^2}[/tex]

    [tex]\angle{H(jw) = TAN^{-1}\frac{w}{2} - TAN^{-1}\frac{5w}{4-w^2}[/tex]


    and that's where things go bad. if the input is 5cos(2t+30) and w=2 then the angle of H(jw) goes to infinity.

    Where am I going wrong here?
     
  2. jcsd
  3. Oct 4, 2007 #2
    What is the LaPlace transform of your input? How do you do a time domain convolution in the frequency domain?
     
  4. Oct 5, 2007 #3
    I found my error, I just plain forgot that arctan infinity was pi/2.
     
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