Laplace Transform

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

  1. lkwah86

    Thread Starter Member

    Mar 9, 2007
    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
    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)

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