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 2 years ago
Find the Laplace transform of the function given by f(t)=2t if t<=2 and f(t)=4 if t>2
 2 years ago
Find the Laplace transform of the function given by f(t)=2t if t<=2 and f(t)=4 if t>2

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Herp_Derp
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. So you split up your integrand into two parts, right?

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0I got 2+(2/(1+s)) and it was wrong

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0\[L\{f(t)\}=\int_{0}^{inf}e^{st}f(t)~dt\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0in this case, you split the integral up into 2 sections

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0I did that and I was wrong :(

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0can you type up your work? then we can see where the mistake might have happened

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0theres a shifting method that i can never remember, so i tend to do it the splitted way

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0yea 2\[2\int\limits_{0}^{2}e^(st)+\int\limits_{0}^{infinity}4e^(st)dt\]

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0it's supposed to be e^(st)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.00,2; then 2,inf for starters; and dont forget your "t" on the left side

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0f(t)=2e^(2s)/s + 2/s

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0oh sorry i actually have that down on my paper but I just typed it wrong

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0\[2\int_{0}^{2}e^{st}t+4\int_{2}^{inf}e^{st}dt\]

Herp_Derp
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \int_0^2 2te^{st}\,dt+\int_0^{\infty}4e^{st}\,dt=2\int_0^2 te^{st}\,dt+4\int_0^{\infty}e^{st}\,dt\]Just making it look better :)

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 thats what I have. What do I do afterwards but thats where I went wrong

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks @Herp_Derp but I have that but afterwards is where I'm confused

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.02 to inf on the last one, the long right term is simple enough; the left side is by parts

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0I know I got that but afterwards is where I'm confused

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0for the firsr part the integral ends up equaling (3(1e^(2s)(2s+1))/(s^2)

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0and the second integral is (e^(2s))/s

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0so (3(1e^(2s)(2s+1))/(s^2) +(e^(2s))/s

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0\[2\int_0^2 te^{st}\,dt+4\int_2^{\infty}e^{st}\,dt\] \[2(~\left.\frac{te^{st}}{s}\right_{t=0}^{t=2}+\frac{1}{s}\left(\int_0^2 e^{st}\,dt\right)+4\left.\frac{e^{st}}{s}\right_{t=2}^{t=inf}\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0this thing aint latex friendly :) \[2\left.\frac{te^{st}}{s}\right_{t=0}^{t=2}+\frac{2}{s}\left(\int_0^2 e^{st}\,dt\right)+4\left.\frac{e^{st}}{s}\right_{t=2}^{t=inf}\] \[2\left.\frac{te^{st}}{s}\right_{t=0}^{t=2}+\left.\frac{2}{s}\frac{e^{st}}{s}\right_{t=0}^{t=2}+4\left.\frac{e^{st}}{s}\right_{t=2}^{t=inf}\] \[2\frac{te^{2s}}{s}2\frac{te^{0}}{s}+\frac{2}{s}\frac{e^{2s}}{s}\frac{2}{s}\frac{e^{0}}{s}+4\frac{e^{s(inf)}}{s}4\frac{e^{2s}}{s}\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0id clean it up a little if i was you

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{2te^{2s}}{s}+\frac{2t}{s}\frac{2e^{2s}}{s^2}+\frac{2}{s^2}+\cancel{4\frac{e^{s(inf)}}{s}}+\frac{4e^{2s}}{s}\] stuff like that

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0great time for loading issues eh

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0\[2\int_{0}^{2}e^{st}t+4\int_{2}^{inf}e^{st}dt\] \[2(\frac{e^{2s}1}{s^2})+4\frac{e^{2s}}{s}\] or some variation of that should work

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0i never did get into the heaviside stuff to be competent enough in that method

ranyai12
 2 years ago
Best ResponseYou've already chosen the best response.0sorry openstuy froze up! an it's still wrong
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