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07-01-2005, 02:27 PM
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#11 |
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Drow Priestess
 Join Date: March 13, 2001
Location: a hidden sanctorum high above the metroplex
Age: 55
Posts: 4,037
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Well, I didn't substitute exactly in the manner you suggest, but that isn't important.
What is important is that my answer might be wrong and yours might be right. My "big plans" of looking into the problem when I got home fell through and then I got really lazy on my day off. [img]tongue.gif[/img] [img]graemlins/petard.gif[/img] hmmm....I found this interesting site which gives the result of cos(sqrt(3)*t) + cosh (sqrt(3) * t). This is going to require a little more investigation.... [ 07-01-2005, 02:38 PM: Message edited by: Azred ]
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Everything may be explained by a conspiracy theory. All conspiracy theories are true. No matter how thinly you slice it, it's still bologna. |
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07-02-2005, 06:35 PM
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#12 |
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Drow Priestess
Join Date: March 13, 2001
Location: a hidden sanctorum high above the metroplex
Age: 55
Posts: 4,037
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And now for the definitive answer....
Begin with the original equation s^2/(s^4 - 9), which breaks down into (s/(s^2 + 3))*(s/(s^2 - 3)). The inverse Laplace of s/(s^2 + 3) is cos (3t) and the inverse Laplace of s/(s^2 - 3) is cosh (3t), therefore... ...the inverse Laplace transform of the original equation is cos(3t) * cosh (3t), taking advantage of the convolution theorem. Of course, s > abs(sqrt(3)). That should end the disussion. [img]graemlins/petard.gif[/img]
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Everything may be explained by a conspiracy theory. All conspiracy theories are true. No matter how thinly you slice it, it's still bologna. |
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07-02-2005, 07:20 PM
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#13 |
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Legion Symbol
 Join Date: February 14, 2002
Location: Ireland
Age: 41
Posts: 7,370
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I'm afraid it dont work that way
take for e.g 1/s^2 can be broken into (1/s) * (1/s) the inverse of 1/s = 1 but the invesre of 1/s^2 is not 1*1
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07-03-2005, 02:04 AM
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#14 |
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Drow Priestess
Join Date: March 13, 2001
Location: a hidden sanctorum high above the metroplex
Age: 55
Posts: 4,037
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Well, I worked it out by hand with my handy differential equations book by my side, but...
...I'm not going to quibble about it. [img]graemlins/petard.gif[/img]
__________________
Everything may be explained by a conspiracy theory. All conspiracy theories are true. No matter how thinly you slice it, it's still bologna. |
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