# Find Laplace Transform

• Nov 4th 2012, 04:44 PM
nak5120
Find Laplace Transform
Hey everyone,
I am having trouble with this question and was hoping someone can show me how it's done.

Find the Laplace transform of the function:
f(t) = coshbt (Note: coshx = (e^x + e^(−x))/2)
• Nov 4th 2012, 05:30 PM
topsquark
Re: Find Laplace Transform
Quote:

Originally Posted by nak5120
Hey everyone,
I am having trouble with this question and was hoping someone can show me how it's done.

Find the Laplace transform of the function:
f(t) = coshbt (Note: coshx = (e^x + e^(−x))/2)

$\displaystyle L{f(t)} = \int_0^{\infty} e^{-st}cosh(bt)~dt$

$\displaystyle = \frac{1}{2} \int_0^{\infty}e^{-st}(e^{bt} + e^{-bt} )~dt$

Are you having problems with this integral?

-Dan
• Nov 4th 2012, 08:51 PM
nak5120
Re: Find Laplace Transform
I understand the general form of it but I don't get why you would put (1/2) (e^(bt)+e^(-bt) in the equation. Is that supposed to be a solution to cosh(bt) somehow?
• Nov 6th 2012, 05:44 PM
topsquark
Re: Find Laplace Transform
Quote:

Originally Posted by nak5120
Hey everyone,
I am having trouble with this question and was hoping someone can show me how it's done.

Find the Laplace transform of the function:
f(t) = coshbt (Note: coshx = (e^x + e^(−x))/2)

You said yourself the definition of cosh(bt). I assumed you would know what that meant when I substituted it in.

The solution is the integral that I posted. If you are having problems with the cosh(bt) substitution somehow?

-Dan