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Azred · 07-02-2005, 06:35 PM

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]

07-02-2005, 06:35 PM	#12
Azred Drow Priestess Join Date: March 13, 2001 Location: a hidden sanctorum high above the metroplex Age: 55 Posts: 4,037	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] __________________ Everything may be explained by a conspiracy theory. All conspiracy theories are true. No matter how thinly you slice it, it's still bologna.