Question

Determine the Laplace transform of the given generalized function. 78(t-3) ${78(t-3)}(s) =

Answer 1

◆ we are given a problem on Laplace transform.

we first take a look on the Laplace transform rule of delta function below:

$L\left \{ \delta (t-a) \right \}=e^{-sa}$

Where , a is positive real number.

Now the given problem is,

L78(t – 3)}

Using the Laplace transform rule given above,

L78(t – 3)}

$=7L\left \{\delta (t-3) \right \}$

$=7e^{-3s}$

therefore the Laplace transform of the given function is 7e^-3s .

Thank you for this beautiful question.