Question

hi guys... bit of a harder Q is anyone has a sec?


Could someone walk me through a laplace transform of :
\[ f(t) = 5u(t) + 5*(e^(-5t))*u(t) + sin(wt)u(t)\]
or a laplace transform of anything? please and thank you.

Answer 1

\[\Large f(t) = 5u(t) + 5e^{-5t}u(t) + sin(wt)u(t)\]

Answer 2

You know the definition of Laplace transform?

Answer 3

yep, integral transform
f(s) = integrate f(t)e ^(-st) dt

Answer 4

OK, so you need help in doing the integration.

Answer 5

yeah... i'm in the southern hemisphere, so i've just gone back to study, and forgotten last semester's work :(
so would love play by play for this, still have the transform tables if that helps?

Answer 6

and what's "s" in this?

Answer 7

Just a complex argument. Look it up on Wikipedia.

Answer 8

gotcha, complex number... but that raises more q's:
what's sigma in this case? (as we have angular speed "w")

Answer 9

I'm not sure. Can you give me more context?

Answer 10

\[ s = σ ~~+~~ iω\] with real numbers σ and ω.

Answer 11

I know this. I assumed there was a reference to ω in the question and was wondering if there's more information about what the function represents

Answer 12

no idea, sorry, just lookin in a workbook of practice q's and this is the first...

Answer 13

So far what I'm imagining is that there will be a little bit of reverse chain rule and product rule here.
It's slowly coming together in my head. I'll explain when I have more.

Answer 14

cools, thanks man

Answer 15

Here's the idea I've got:\[{d \over dx}f(x)e^{-ax}=(f'(x)-af(x))e^{-ax}\]I'm trying to separate the expression into a bunch of functions and derivatives and reverse this.

Answer 16

The trigonometric function can be done with harmonic form, I think.

Answer 17

The u(t) which was splodged on will be significantly more fun.

Answer 18

sploged...?
an u and i have verrrrrrrry different ideas about fun mate ;D

Answer 19

so with this statement:
"The trigonometric function can be done with harmonic form"
u lost me at harmonic form...

Answer 20

OK, my plan was to split the sin like this:\[\sin(wt)={1 \over \sqrt2}(\sin(w(t-\pi/4))+cost(w(t-\pi/4))\]

Answer 21

The idea is that trigonometric functions are derivatives of each other.

Answer 22

We slide the two bits along until the coefficient of the appropriate one is a factor of w greater than the other.

Answer 23

Then we shall have our function and derivative.

Answer 24

o...kay...

Answer 25

You seem unsure. I shall explain anything which is unclear to you if you point it out to me.

Answer 26

ok, why split before we integrate?

Answer 27

Crud, I just realised I made a stupid mistake with my reasoning. That was a good question. And the answer is, we don't. Because my brain has just had one of those dumb moments. I'm sorry about that. This happens when I bounce round ideas in my head.

Answer 28

all good man, ur still 4 steps ahead of me... im trying to remember integration ;D

Answer 29

Do you recall integration by parts?

Answer 30

not off-hand... actually i remember i struggled with that, sorry.

Answer 31

It's a reverse of the product rule:
\[(uv)′=u′v+uv′\]
Therefore:
\[∫u′v=uv−∫uv′\]

Answer 32

ok, with u so far

Answer 33

Do you recall using integration by parts on such things as a product of a polynomial and some exponential function?

Answer 34

yes, but i also recall failing at it. can integrate loads of different stuff, but always failed when it came to partial integration for some reason.

Answer 35

I imagine that was due to the silly mistakes of not keeping track of plus/minus signs and which things to differentiate/integrate. Happened to me too. If you stay focused, you should pull through. Now, let's go and integrate this basterd by parts!

Answer 36

dude, confession time, i posted this q in like 4 different maths sections, haveing a bit of luck in this one (using the tables) thank you for the help but i'm going to go with this one for the moment, come join us if u like? http://openstudy.com/study#/updates/531f0885e4b0cf9a45eae7d4