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Use partial fractions or the convolution theorem and the table of Laplace transforms, to find functions of \(t\) which have the following Laplace transforms.
(b) \[\frac{p+2}{2p^2+p1}\]
 one year ago
 one year ago
Use partial fractions or the convolution theorem and the table of Laplace transforms, to find functions of \(t\) which have the following Laplace transforms. (b) \[\frac{p+2}{2p^2+p1}\]
 one year ago
 one year ago

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UnkleRhaukusBest ResponseYou've already chosen the best response.0
(b) partial fractions \[\begin{align*} F(p)&=\frac{p+2}{2p^2+p1}\\ &=\frac{p+2}{(p+1)(2p1)}&=\frac{A}{p+1}+\frac{B}{2p1}\\ \\&&p+2=A(2p1)+B(p+1)\\ \\&\text{for } p=1&1=3A\\ &&A=\tfrac{1}3\\ \\&\text{for } p=0&2=A+B\\ &&B=2\tfrac 13=\tfrac53\\ \\ F(p)&=\frac{\tfrac13}{p+1}+\frac{\tfrac53}{2p1}\\ &=\tfrac13\left(\frac{5}{2p1}\frac{1}{p+1}\right)\\ \\ f(t)&=\tfrac13\mathcal L^{1}\left\{\frac{5}{2p1}\frac{1}{p+1}\right\}\\ &=\tfrac13\left(\tfrac52\mathcal L^{1}\left\{\frac{1}{p\tfrac12}\right\}\mathcal L^{1}\left\{\frac1{p+1}\right\}\right)\\ &=\tfrac13\left(\tfrac52e^{t/2}e^{t}\right)\\ \\ &=\frac56e^{t/2}\frac13e^{t}\\ \end{align*} \]
 one year ago

malevolence19Best ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=inverse+laplace+transform+of+%28s%2B2%29%2F%282s%5E2%2Bs1%29
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
what do i do with that/??
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
im having trouble with deconvolution
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1353549631736:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1353549766387:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1353549812275:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1353550099053:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1353550140216:dw
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
(b) table of laplace transforms \[\begin{align*} F(p)&=\frac{p+2}{2p^2+p1}\\ &=\frac{p+2}{(2p1)(p+1)}\\ &=\tfrac12\times\frac{p}{(p\tfrac12)(p+1)}+\frac{1}{(p\tfrac12)(p+1)}\\ f(t)&=\tfrac12\mathcal L^{1}\left\{\frac{p}{(p\tfrac12)(p+1)}\right\}+\mathcal L^{1}\left\{\frac{1}{(p\tfrac12)(p+1)}\right\}\\ &=\tfrac12\times\frac{1/2e^{t/2}+e^{t}}{1/2+1}+\frac{e^{t/2}e^{t}}{1/2+1}\\ &=\tfrac12\times\frac{1/2e^{t/2}+e^{t}}{3/2}+\frac{e^{t/2}e^{t}}{3/2}\\ &=\tfrac13\times\left(1/2e^{t/2}+e^{t}\right)+\tfrac23{e^{t/2}\tfrac23e^{t}}\\ &=\tfrac16e^{t/2}+\tfrac13e^{t}+\tfrac23{e^{t/2}\tfrac23e^{t}}\\ &=\frac56e^{t/2}\frac13e^{t} \end{align*}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
the derivative fo the dirac delta is not familiar to me
 one year ago

malevolence19Best ResponseYou've already chosen the best response.0
Yeah, I was wondering the same thing. How is \[\delta ' (t)\] defined?
 one year ago
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