Inverse Laplace transform for 1/(350+s) * X(s)

[DinaZhang1]

Hi, everyone, the question is as below:

Find the inverse Laplace transform to 1/(350+s) * X(s). 's' is the Laplace variable and 'X(s)' is also a variable.

I inverted 1/(350+s) and X(s) separately and multiplied them together directly. But this seems not giving me the correct answer. Could anyone help me on this?

Thank you.

 

[Ray Vickson]

Hi, everyone, the question is as below:

Find the inverse Laplace transform to 1/(350+s) * X(s). 's' is the Laplace variable and 'X(s)' is also a variable.

I inverted 1/(350+s) and X(s) separately and multiplied them together directly. But this seems not giving me the correct answer. Could anyone help me on this?

Thank you.

Multiplication won't work; you need convolution.

If $f(t) \leftrightarrow F(s)$ and $g(t) \leftrightarrow G(s)$, then $F(s) G(s)$ is the Laplace transform of the convolution $f*g$, where
$$(f * g)(x) = \int_0^{\infty} f(y) g(x-y) \, dy = \int_0^{\infty} f(x-y) g(y) \, dy .$$