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Laplace transforms

  1. Mar 24, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm given the transfer function of LTI system is [itex]\frac{1}{s^2 + 4}[/itex]

    2. Relevant equations

    H(s) = [itex]\frac{Y(s)}{X(s)}[/itex]

    3. The attempt at a solution

    first of all I had to find diff. equations of the system. I found that it's y'' + 4*y = x;
    Then they asked to find such initial conditions that if I applied unit impulse at input, I got y=0 for time t>=0; I took Laplace transform of diff. equation with initial conditions and got that s^2Y - sY(0) - Y'(0) + 4Y = 1; I want y=0, so Y=0 and 1+sY(0) + Y'(0) = 0; I'm wrong in something....
     
  2. jcsd
  3. Mar 24, 2013 #2
    Matlab

    Code (Text):
    syms y(t) x(t) a t
    Dy = diff(y);
    A = dsolve(diff(y, 2) + 4*y == dirac(t), y(0) == 0, Dy(0) == -1);
    ezplot(A, [0 10])

    pretty(laplace(A))
    I get something slightly different in matlab
     
  4. Mar 24, 2013 #3
  5. Mar 24, 2013 #4
    Thanks milesyoung, it helped!
     
  6. Mar 24, 2013 #5

    rude man

    User Avatar
    Homework Helper
    Gold Member

    You should use y for the time functions and Y for the transformed variables.

    You are right in saying y(0+) = 0 but what about y'(0+)?
     
  7. Mar 24, 2013 #6
    He/she wrote the correct initial conditions in the code segment.
     
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