# laplace of two function?

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• January 6th 2011, 09:59 AM
Hamed
laplace of two function?
Hello,
I need laplace transform of these function:
f(t)=(t^n)cos(a*t)
and
f(t)=(t^n)cosh(a*t)
• January 6th 2011, 10:14 AM
Ackbeet
For the first, note that

$\mathcal{L}\left[t^{n}f(t)\right]=(-1)^{n}\dfrac{d^{n}}{ds^{n}}\,F(s),$

and

$\mathcal{L}\left[\cos(at)\right]=\dfrac{s}{s^{2}+a^{2}}.$

For the second, note in addition that

$\mathcal{L}\left[\cosh(at)\right]=\dfrac{s}{s^{2}-a^{2}}.$

Where does that get you?
• January 6th 2011, 08:37 PM
Hamed
I want to make laplace transform table to memorize them.