What Is the Laplace Transform of a Convolution?

[rj18]

Homework Statement

hey i was wondering if i could get some help with my maths i need to find the output using place and then convolution . i need to find out the step input response and how to use convolution to find output when input = [0,t<0 t,0<t<t1 t1,t<0<t2]

thanks

Relevant Equations

Laplace equation was s^2+5s+8=(1/s+2)
inverse 1/4 e^(-2t)-1/4 e^(-2t)+e^(-2t)/2 t
find concolution when input = [0,t<0 t,0<t<t1 t1,t<0<t2]

e

 

[scottdave]

So do you recall what the Laplace Transform of {f(t) • g(t) } is? Where I used the • to represent convolution.
This may help -
https://www.rapidtables.com/math/calculus/laplace_transform.html#Laplace transform properties

 

[rj18]

i meant convolution*
and yes i have used convolution in problems that are shorter and much simpler. such as for the input t<0. but i don't know how to do it with more input variables such as 0<t<t1

 

[LCKurtz]

Homework Statement: hey i was wondering if i could get some help with my maths i need to find the output using place and then convolution . i need to find out the step input response and how to use convolution to find output when input = [0,t<0 t,0<t<t1 t1,t<0<t2]

That string of variables and commas etc. doesn't mean anything to me.

thanks
Homework Equations: Laplace equation was s^2+5s+8=(1/s+2)

Is that supposed to represent a transform of something? It doesn't make any sense as it is written.

inverse 1/4 e^(-2t)-1/4 e^(-2t)+e^(-2t)/2 t
find concolution when input = [0,t<0 t,0<t<t1 t1,t<0<t2]

What is that supposed to be the inverse of? Your post is hopelessly confusing. You could start by stating the original problem word for word.

 

[rj18]

So do you recall what the Laplace Transform of {f(t) • g(t) } is? Where I used the • to represent convolution.
This may help -
https://www.rapidtables.com/math/calculus/laplace_transform.html#Laplace transform properties

So do you recall what the Laplace Transform of {f(t) • g(t) } is? Where I used the • to represent convolution.
This may help -
https://www.rapidtables.com/math/calculus/laplace_transform.html#Laplace transform properties

That string of variables and commas etc. doesn't mean anything to me.

Is that supposed to represent a transform of something? It doesn't make any sense as it is written.

What is that supposed to be the inverse of? Your post is hopelessly confusing. You could start by stating the original problem word for word.

Sorry that i wasnt clear enough
i found the laplace transform and the impulse response i think.
i have given all the questions a go but not too sure