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 2 years ago
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.
 2 years ago
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.

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eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0Is the 'del' symbolic of using the delta function?

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0Could you please explain the logic you approach this with and how you handled the intervals where the function equaled a constant?

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0In my textbook, the delta function is not introduced for 4 more sections.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2Do you know extended derivative with delta function?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2Mathematician said there is no derivative in uncontinious point but engineers said it has.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2@ali110 is one of them.

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0So far what I know of piecewise functions is that L{f(x)} = L{f_1(x)} + L{f_2(x)} + L{f_3(x)}

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2no, there is no information in an alone point for Laplace, but I made derivative to make an information then used the Laplace.

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0How did you make a derivative of a function that has only a constant value?

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0L(f(t))=L(1)=1/s if for f(t)=t then L(f(t))=1/s^2

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2@ali110 is one of them.

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0mohan gholami in which of them?

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0If it never equals 't', then do I only have \[\frac{1}{s} +\frac{1}{s} +\frac{1}{s}\] ?

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0I believe he was saying that you were an engineer.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2No, you have two points not two functions!

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0oh i am an electrical engineering student of 5th semester who got 71 marks out of 100 in laplace transform in his 4th semster:))) @eSpeX

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2Unfortunately Laplace transform doesn't sense points unless with delta function.

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0Laplace 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?

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0L(f(t))=L(3)=3L(1)=3*1/s=3/s

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0According to the book, the answer is 1/s. Does this mean that the laplace of t=1 and t=2 equate to 0?

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0can we take laplace inverse at the end?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2No 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
 2 years ago
Best ResponseYou've already chosen the best response.0So you would have: L{f(t)} = L{1} + L{3} + L{4} > 1/s + 0 + 0 ?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2ok I solve it with integral. int(0 inf) f(t)=1/s

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2You know the integral change the limit points to continues function and never sense them.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.21 f'(t)=3del(t1)3del(t1)+4del(t2)4del(t2) and f(0)=1 L(f'(t))=3e^s3e^s+4e^2s4e^2s=sL(f(t))1 L(f(t))=1/s(0+0+1)=1/s

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2I thought in two points 1 and 2 it has jumped so they were two alone points.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2And Laplace has problem with the single points.

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0Ah. Okay, I will see if I can't apply this to the rest of my problems. Thank you very much.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2if the points in 1 and 2 was jumped so the solution was : 1 f'(t)=3del(t1)+4del(t2) 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
 2 years ago
Best ResponseYou've already chosen the best response.0But at this point I would have needed to use the integral approach since we have not reached the delta function?

eSpeX
 2 years ago
Best ResponseYou've already chosen the best response.0It appears that all of those examples have a range that the integral is evaluated over. So none of the laplace methods evaluate a point.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2But @ali110 there is no unit step and delta function! I guess Openhiem is the best refrence. Isn't it?

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0check 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

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0L{f(t)} = L{1} + L{3} + L{4} > 1/s + 0 + 0=1/s

ali110
 2 years ago
Best ResponseYou've already chosen the best response.0@eSpeX CHECK laplace transform linearity property (in which one to one property)

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2Ok. 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
 2 years ago
Best ResponseYou've already chosen the best response.0Alright, I'll have to look up limit points then because I have not seen them yet as I recall.

KenLJW
 one year ago
Best ResponseYou've already chosen the best response.0You have to use the unit step function for 2 and 3 3u(t1) 4u(t2) for the first one I'd break it up u(t1)  u(t1minus) + u(t1 plus) u(t2 minus) ect With these there's direct transformations

KenLJW
 one year ago
Best ResponseYou've already chosen the best response.0In 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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