Let me get back home from work this evening and I'll have an answer for you. [img]graemlins/petard.gif[/img]
On second thought I decided not to wait.
Substitute k = s^2 so that the problem becomes k/(k^2 - 9) and a quick check of an online Laplace table shows the transform of cosh (at) for k > abs(a). Since k = s^2, this becomes s > abs(sqrt(a)) or in this case s > abs(sqrt(3)).
For those who haven't studied engineering, the hyperbolic cosine has the interesting property that the transverse forces acting on a hyperbolic cosine curve turn out to be zero. That is to say, the only sources of stress occur in the same dimension as the line of symmetry so that if an arch is built in the form of a hyperbolic cosine only gravity exerts stress on the arch...like the Gateway Arch in St. Louis.
[ 06-29-2005, 09:16 PM: Message edited by: Azred ]
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