Heaviside Function Homework: Laplace Transform w/ Right Shift

[cragar]

Homework Statement

how to i take the laplace transform of this ,

-tH(t-1)

so we need to get thr right shift so is it -(t-1 + 1 ) so do i take the laplace transform of
-(t+1) so would it be -(1/s^2 + 1/s ) *e^(-s)

 

[CompuChip]

You just need to calculate
- \int_0^\infty e^{-s t} t H(t - 1) \, \mathrm dt

You can break up the integral in two parts: 0 < t < 1 and t > 1.

 

[cragar]

we can't just force the shift , if we had t^2H(t-1)
then to shift the quadratic we would (t-2+2)^ then we would expand
(t+2)^2 to t^2+4t+4 then take the laplace transform of that .

 

[CompuChip]

What do you want to shift? H(t - 1) is zero for t < 1, so

<br /> \int_0^\infty f(t) H(t - 1) \, \mathrm dt<br /> =<br /> \int_0^1 0 \cdot f(t) \, \mathrm dt + \int_1^\infty 1 \cdot f(t) \, \mathrm dt<br /> =<br /> \int_1^\infty f(t) \, \mathrm dt<br />
or am I really stupid?

 

[cragar]

um i don't know my teacher never really talked about it like that,
ur prolly right , and another thing i can't see what ever u typed in those black boxes
my computer won't let me so its hard for me to tell what ur doing .

I am sure ur right , but my teacher told us to take the laplace tranform
of a function time the heaviside function
he said the function needed to have the same shift as the heaviside
function in order for the formula to work .
f(t)H(t-1) = e^(-s)*L(f(t))