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johnny0929 Group Title

laplace transform of \[f(t)=u_1(t)+2u_3(t)-6u_4(t)\]and the answer is \[F(s)=s^{-2}[(1-s)e^{-2s}-(1+s)e^{-3s}]\]but I dont know how to get this

  • one year ago
  • one year ago

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  1. johnny0929 Group Title
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    All I know is that the laplace of \(u_c(t)\)=\[\frac{e^{-cs}}{s}\]

    • one year ago
  2. Mertsj Group Title
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    Have to get the smart guys to help you with this.

    • one year ago
  3. modphysnoob Group Title
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    well, you got the table right?

    • one year ago
  4. johnny0929 Group Title
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    so with the identity I have \[F(s)=\frac{e^{-s}}{s}+2\frac{e^{-3s}}{s}-6\frac{e^{-4s}}{s}\]and how do I make it look like the answer I have above?

    • one year ago
  5. johnny0929 Group Title
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    and yes i do have the table

    • one year ago
  6. modphysnoob Group Title
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    alright, let's try something different

    • one year ago
  7. johnny0929 Group Title
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    i have another identity regarding step functions, it's this \[u_c(t)f(t-c)=>e^{-cs}F(s)\]

    • one year ago
  8. modphysnoob Group Title
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    do you know how they look like though?

    • one year ago
  9. johnny0929 Group Title
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    yeah i think

    • one year ago
  10. modphysnoob Group Title
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    |dw:1364173680082:dw|

    • one year ago
  11. johnny0929 Group Title
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    guys i apologize sincerely....... it looks like I have read the wrong answer to the problem......

    • one year ago
  12. modphysnoob Group Title
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    ok, that happens

    • one year ago
  13. johnny0929 Group Title
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    sorry and thanks for your help!!

    • one year ago
  14. UnkleRhaukus Group Title
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    i was gonna say...

    • one year ago
  15. UnkleRhaukus Group Title
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    \[f(t)=u_1(t)+2u_3(t)-6u_4(t)\] \[\mathcal L\big\{f(t)\big\}=\mathcal L\big\{u_1(t)\big\}+2\mathcal L\big\{u_3(t)\big\}-6\mathcal L\big\{u_4(t)\big\}\\\qquad\qquad=\frac {e^{-s}}s+2\frac {e^{-3s}}s-6\frac {e^{-4s}}s\\\qquad F(s)=\frac1s\big(e^{-s}+2e^{-3s}-6e^{-4s}\big)\]

    • one year ago
  16. nincompoop Group Title
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    table looks like this |dw:1364174488647:dw|

    • one year ago
  17. nincompoop Group Title
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    jk

    • one year ago
  18. UnkleRhaukus Group Title
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    |dw:1364174630421:dw|

    • one year ago
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