eSpeX
  • eSpeX
Laplace Transform: Evaluate L{f(t)} \[\begin {align*} f(t) &= 1 ,\ t \ge 0, \quad t \neq 1, \ t \neq 2 \\ &= 3,\ t = 1\\ &= 4,\ t = 2\end {align*} \] Would appreciate someone explaining how to set this up and evaluate.
Mathematics
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katieb
  • katieb
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eSpeX
  • eSpeX
Is the 'del' symbolic of using the delta function?
anonymous
  • anonymous
Absolutely yes.
eSpeX
  • eSpeX
Could you please explain the logic you approach this with and how you handled the intervals where the function equaled a constant?

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eSpeX
  • eSpeX
In my textbook, the delta function is not introduced for 4 more sections.
anonymous
  • anonymous
Do you know extended derivative with delta function?
anonymous
  • anonymous
Mathematician said there is no derivative in uncontinious point but engineers said it has.
anonymous
  • anonymous
@ali110 is one of them.
eSpeX
  • eSpeX
So far what I know of piecewise functions is that L{f(x)} = L{f_1(x)} + L{f_2(x)} + L{f_3(x)}
eSpeX
  • eSpeX
Those should be f(t)...
anonymous
  • anonymous
no, there is no information in an alone point for Laplace, but I made derivative to make an information then used the Laplace.
eSpeX
  • eSpeX
How did you make a derivative of a function that has only a constant value?
anonymous
  • anonymous
L(f(t))=L(1)=1/s if for f(t)=t then L(f(t))=1/s^2
anonymous
  • anonymous
@ali110 is one of them.
anonymous
  • anonymous
mohan gholami in which of them?
eSpeX
  • eSpeX
If it never equals 't', then do I only have \[\frac{1}{s} +\frac{1}{s} +\frac{1}{s}\] ?
eSpeX
  • eSpeX
I believe he was saying that you were an engineer.
anonymous
  • anonymous
No, you have two points not two functions!
anonymous
  • anonymous
oh i am an electrical engineering student of 5th semester who got 71 marks out of 100 in laplace transform in his 4th semster:))) @eSpeX
anonymous
  • anonymous
Unfortunately Laplace transform doesn't sense points unless with delta function.
eSpeX
  • eSpeX
Laplace does not make sense to me on how to handle them, and with respect to this piecewise I do not see how it will be done if we have not been shown the delta function. Is it something (or similar) to the heavyside step function?
anonymous
  • anonymous
L(f(t))=L(3)=3L(1)=3*1/s=3/s
eSpeX
  • eSpeX
According to the book, the answer is 1/s. Does this mean that the laplace of t=1 and t=2 equate to 0?
anonymous
  • anonymous
can we take laplace inverse at the end?
anonymous
  • anonymous
No the answer is just 1/s because Laplace transform can not sense limit points, and it just follow the infinity points which defined with delta function.
eSpeX
  • eSpeX
So you would have: L{f(t)} = L{1} + L{3} + L{4} -> 1/s + 0 + 0 ?
anonymous
  • anonymous
ok I solve it with integral. int(0 inf) f(t)=1/s
anonymous
  • anonymous
You know the integral change the limit points to continues function and never sense them.
anonymous
  • anonymous
1 f'(t)=3del(t-1)-3del(t-1)+4del(t-2)-4del(t-2) and f(0)=1 L(f'(t))=3e^-s-3e^-s+4e^-2s-4e^-2s=sL(f(t))-1 L(f(t))=1/s(0+0+1)=1/s
anonymous
  • anonymous
I thought in two points 1 and 2 it has jumped so they were two alone points.
anonymous
  • anonymous
And Laplace has problem with the single points.
eSpeX
  • eSpeX
Ah. Okay, I will see if I can't apply this to the rest of my problems. Thank you very much.
anonymous
  • anonymous
You're welcome.
anonymous
  • anonymous
if the points in 1 and 2 was jumped so the solution was : 1 f'(t)=3del(t-1)+4del(t-2) and f(0)=1 L(f'(t))=3e^-s+4e^-2s=sL(f(t))-1 L(f(t))=1/s(3e^-s+4e^-2s+1)
eSpeX
  • eSpeX
But at this point I would have needed to use the integral approach since we have not reached the delta function?
anonymous
  • anonymous
1 Attachment
eSpeX
  • eSpeX
It appears that all of those examples have a range that the integral is evaluated over. So none of the laplace methods evaluate a point.
anonymous
  • anonymous
But @ali110 there is no unit step and delta function! I guess Openhiem is the best refrence. Isn't it?
anonymous
  • anonymous
check page 11 and every problem will solve as writer show that for t not equal to 1 And 2 as in above question F=0 and Agha! i love alan V openheim as i take all his video lectures about signals and systems but in our engineerig college we study Indian professor Ghosh sumarjit check his book on Signal and system and about fourier series more intersesting then oppenheim
anonymous
  • anonymous
@mahmit2012
anonymous
  • anonymous
L{f(t)} = L{1} + L{3} + L{4} -> 1/s + 0 + 0=1/s
anonymous
  • anonymous
@eSpeX I GUESS
anonymous
  • anonymous
@eSpeX CHECK laplace transform linearity property (in which one to one property)
eSpeX
  • eSpeX
Okay.
anonymous
  • anonymous
Ok. And I should mention that don't use L(3)=0 because it is not true. You can write L*(3)=0 and define L* means Laplace for limit points.
eSpeX
  • eSpeX
Alright, I'll have to look up limit points then because I have not seen them yet as I recall.
KenLJW
  • KenLJW
You have to use the unit step function for 2 and 3 3u(t-1) 4u(t-2) for the first one I'd break it up u(t-1) - u(t-1minus) + u(t-1 plus) -u(t-2 minus) ect With these there's direct transformations
KenLJW
  • KenLJW
In EE the slope of the step function is an indication of bandwidth, if there was infinite bandwidth it would be a unit step

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