Hello,

I need laplace transform of these function:

f(t)=(t^n)cos(a*t)

and

f(t)=(t^n)cosh(a*t)

Printable View

- Jan 6th 2011, 08:59 AMHamedlaplace 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) - Jan 6th 2011, 09:14 AMAckbeet
For the first, note that

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

and

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

For the second, note in addition that

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

Where does that get you? - Jan 6th 2011, 07:37 PMHamed
I want to make laplace transform table to memorize them.