Laplace transform of Heaviside function

[gravenewworld]

Homework Statement

What is the laplace transform of H(-t-17)

Homework Equations

Shifting theorem:

L(H(t-a)) = (e^-as)/s

The Attempt at a Solution

This is the only part of the problem that I can not get (this part is from a larger differential equation I'm trying to solve). I'm can't seem to figure out how the Laplace transform changes if there is a negative sign in front of the t. I'm not sure if there are some properties of the Heaviside function that will allow me to solve this that I simply don't know and that we didn't go over in class.

 

[Mark44]

Homework Statement

What is the laplace transform of H(-t-17)

Homework Equations

Shifting theorem:

H(t-a) = (e^-at)/s

The Attempt at a Solution

This is the only part of the problem that I can not get (this part is from a larger differential equation I'm trying to solve). I'm can't seem to figure out how the Laplace transform changes if there is a negative sign in front of the t. I'm not sure if there are some properties of the Heaviside function that will allow me to solve this that I simply don't know and that we didn't go over in class.

It's "Heaviside" which is now fixed.

Your relevant equation is incorrect and has two errors. It should be L(H(t - a)) = (e^-as)/s.

H(t) is the unit step function. H(t - a) is the translation of the unit step function by a units. H(-t - 17) = H(-(t + 17)). This involves a reflection across the vertical axis, followed by a translation to the left by 17 units.

 

[pasmith]

Homework Statement

What is the laplace transform of H(-t-17)

Homework Equations

Shifting theorem:

L(H(t-a)) = (e^-as)/s

The Attempt at a Solution

This is the only part of the problem that I can not get (this part is from a larger differential equation I'm trying to solve). I'm can't seem to figure out how the Laplace transform changes if there is a negative sign in front of the t. I'm not sure if there are some properties of the Heaviside function that will allow me to solve this that I simply don't know and that we didn't go over in class.

If $t > 0$ then $-t -17 < 0$ so $H(-t-17) = 0$ for all $t > 0$. Since the Laplace transform only cares about the values of a function in $t > 0$ the Laplace transform of $H(-t-17)$ is equal to the Laplace transform of the zero function.

 

[gravenewworld]

Thank you both. I was actually able to pull up a nice identity online for H(x), where H(x) = (x + |x|)/2x. It helped a lot as well.