Find the inverse Laplace transform of
$$F(s)=\frac{3se^{-5s}}{s^2-8s+20}$$

Question

Find the inverse Laplace transform of
$$F(s)=\frac{3se^{-5s}}{s^2-8s+20}$$

mendicant_bias · Answer

Yo, you still hurr bb?

mendicant_bias · Answer

(Don't ask me why I said that, I'm just.....yeah.)


Alright, this looks legitimately not fun. So, I can suggest some things immediately if you maybe haven't already thought of them. See the e^{as} term? What do you think will be relevant in the transform because of that term?

mendicant_bias · Answer

(I actually just took a test on totally relevant material, and I made a mistake specifically on a problem like this. I figured out afterwards.)

>:C

anonymous · Answer

$$F(s)=\left(e^{-5s}\frac{3s}{s^2-8s+20}\right)$$

Then whats the next step coz am stuck right here and confused

anonymous · Answer

Am not understanding this chapter at all.

mendicant_bias · Answer

Yeah, man, I had a hell of a time with it, too. That's a step in the right direction. I always get them confused in effect, but separating that e^{as} term will allow you to invoke either the Dirac Delta function, or the Unit Step/Heaviside function.

mendicant_bias · Answer

Alright, so that was a good first step. Now, you should consider how to treat the rest of the problem. Consider your remaining fraction as a standalone problem; do you have an idea of how you might solve it?

anonymous · Answer

$$\frac{ 3s }{ (s-4)^2+4 }$$
I completed the square. then am not sure if it is $$e^{at} sin bt$$ or $$e^{at} cos bt$$

mendicant_bias · Answer

There's no real mnemonic or memory tool I choose to remember it by, but the way I remember it as is that the one with the constant in the numerator is *always* the laplace of the sine function.

The one with s in the numerator is *always* the laplace of the cosine function.

mendicant_bias · Answer

(Sorry for all but abandoning you on this problem for a while; I had some stuff going on and I got distracted.)

Let me know when you come back if you still need help on this.

anonymous · Answer

@Mendicant_Bias I still need your help

mendicant_bias · Answer

Alright, the next time we're both on at the same time, do you understand which trig function it would be?

anonymous · Answer

i havent gotten anywhere on this problem. any hints?