Laplace Transform problem

Mechaman

New member
Joined
Feb 7, 2015
Messages
13
IMG_20191007_084417__01.jpg

I'm having trouble using this Laplace transform. The rule is on the second line that I'm supposed to use but can't see where each part of it applies. I'm using arrows to show where I think each part translates to.

The y(t-a) refers to whatever is in the brackets except for the constants? And the u(t-a) refers to the e term before that?

Also the forth line, Y = e... Is this making a Laplace of an inverse Laplace? How did this go back to capital Y
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
5,286
The first thing I would do is take out the "\(\displaystyle \frac{1}{3}\)":
\(\displaystyle Y(x)= \frac{1}{3}\left(e^{-3s}\left(\frac{1}{s}- \frac{1}{s+ 3}\right)\right)+ \frac{1}{s+ 3}\).

Now distribute the "\(\displaystyle e^{-3s}\)": \(\displaystyle \frac{1}{3}\left(\frac{1}{s}e^{-3s}- \frac{1}{s+3}e^{-3s}\right)+ \frac{1}{s+ 3}\).

Apply your rule to both \(\displaystyle \frac{1}{3}e^{-3s}\) and \(\displaystyle \frac{1}{s+3}e^{-3s}\).
 
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