Question

Hi! I need some help with Laplace transformations :)
It's pretty basic, I just need to know how to transform t-3 :P

Answer 1

\[L\left\{ t-3\right\}=?\]

Answer 2

Do I separate it like this:\[L \left\{ t-3 \right\}=L \left\{ t \right\}-L \left\{ 3 \right\}\]?

Answer 3

or\[\lim_{T \rightarrow \infty}\int\limits_{0}^{T}(t-3)e ^{-st}dt\]

Answer 4

just plug that into ithe integral and evaluate ?

Answer 5

Hm, ok, I'll try :P

Answer 6

or you could use \[\large 1\leadsto \dfrac{1}{s}\]

Answer 7

and the fact that the transform is linear

Answer 8

L(3) = 3*L(1) = 3/s

Answer 9

So\[L \left\{ t-3 \right\}=L \left\{ t \right\}-L \left\{ 3 \right\}=L \left\{ t \right\}-3L \left\{ 1 \right\}\]\[=\frac{ 1 }{ s ^{2} }-\frac{ 3 }{ s }\] ?

Answer 10

looks good !

Answer 11

Thanks!^^

Answer 12

np :)