Laplace Transform

Discussion in 'Math' started by lkwah86, Mar 17, 2007.

  1. lkwah86

    Thread Starter Member

    Mar 9, 2007
    22
    1
    Find the response y(t) of an LITC system described by the equation
    [(d^2)y/(dt^2)] + 5[(dy)/(dt)] + 6y(t) = [(df)/(dt)] + f(t)
    if the input f(t) = 3e^(-5t).u(t) and all the initial conditions are zero;
    that is, the system is in zero-state.

    i duno right hand side how 2 do...
     
  2. DrNick

    Active Member

    Dec 13, 2006
    110
    2
    first of all take the laplace transform of f(t). this would be

    F(s) = 3/(s + 5)

    now take the laplace transform of your ODE

    remember derivatives are just multiplications by s (when there are no initial conditions), so the ODE becomes

    s^2*Y(s) + 5*s*Y(s) + 6Y(s) = 3*s/(s+5) + 3/(s+5).

    note that df/dt => s*(F(s))
    d^2y/dt^2 => s^2Y(s)
    etc...

    Now solve for Y(s)
    =>
    Y(s) = [ 3*s/(s+5) + 3/(s+5) ] * 1/(s^2+5s+6)

    now all you need to do is perform a partial fraction expantion on this, and then inverse transform!!
     
  3. lkwah86

    Thread Starter Member

    Mar 9, 2007
    22
    1
    but the f(t)=3e^(-5t)u(t)....
    behind got u(t)...
    if f(t)=3e^(-5t), answer is 1/(s+5)
     
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