Calculating laplace transforms

Calculating laplace transforms

Lessons

Theorem:

If we have the Laplace Transform of two functions:

LL{f(t)f(t)} = FF(ss)

LL{g(t)g(t)} = GG(ss)

With a,ba,b being constants, then we will have the following:

LL{ af(t)af(t) + bg(t)bg(t)} = aF(s)aF(s) + bG(s)bG(s)

  • 1.
    The Laplace Transform is a linear operator, and defining the Laplace Table

  • 2.
    Determining Laplace Transforms

    Calculate the following Laplace Transforms:

    a)
    LL{3e3t3e^{3t}}

    b)
    LL{sin(3t)+2t\sin(3t) + 2t}

    c)
    LL{4sin(2t)34\sin(2t) - 3}


  • 3.
    What is LL{tnt^{n}}?

  • 4.
    Using the Laplace Transform Table

    Using the Laplace Transform Table calculate the following Laplace Transforms:

    a)
    LL{2sinh(3t)\sinh(3t)}

    b)
    LL{t e3te^{3t} - 2cos(3t)\cos(3t)}

    c)
    LL{e2te^{2t}sin(t)\sin(t) - 15\frac{1}{5}t5t^{5} + 2e3te^{3t}}