A friend of mine needs to take the inverse laplace transform of ((1/s)(1/cosh(s^.5))cosh((s^.5)*x)), bringing s to the t domain. I’ve only been exposed to laplace transforms for one week, so I couldn’t do much. If anyone knows of the appropriate methods or has a link to the necessary tables it would be greatly appreciated.
Thanks!
I opened this thread because I’d thought it said “lapdance.”
Carry on.
Use Wolfram Alpha.
I haven’t had to derive a Laplace transform in thirty years, though I use them often in circuit analysis. As I remember, it’s just a matter of meticulous cranking through the integral. With hairy integrations such as these, integration-by-parts is your best friend. Khan Academy has some excellent videos beginning with this one.
Is this even well-defined? How do you integrate s over the negative part of its range (-∞ to 0) when you have a square root in the function? I suppose you could use the identity that cosh(ix) = cos x, but it seems to me that some care is required.
Is this a homework problem, or something that arose outside of a classroom?