# Calculating laplace transforms

### Calculating laplace transforms

#### Lessons

Theorem:

If we have the Laplace Transform of two functions:

$L${$f(t)$} = $F$($s$)

$L${$g(t)$} = $G$($s$)

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

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

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

• 1.
Determining Laplace Transforms

Calculate the following Laplace Transforms:

a)
$L${$3e^{3t}$}

b)
$L${$\sin(3t) + 2t$}

c)
$L${$4\sin(2t) - 3$}

• 2.
What is $L${$t^{n}$}?

• 3.
Using the Laplace Transform Table

Using the Laplace Transform Table calculate the following Laplace Transforms:

a)
$L${2$\sinh(3t)$}

b)
$L${t $e^{3t}$ - 2$\cos(3t)$}

c)
$L${$e^{2t}$$\sin(t)$ - $\frac{1}{5}$$t^{5}$ + 2$e^{3t}$}