1. ## 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)

2. ## Re: Find Laplace Transform

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

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

Are you having problems with this integral?

-Dan

3. ## 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?

4. ## Re: Find Laplace Transform

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