What is the Laplace Transform of sinh(bt)?

[myusernameis]

Homework Statement

L{sinh(bt)}

Homework Equations

sinh(bt)=(e^bt-e^-bt)

The Attempt at a Solution

so the answer says it's b/(s^2-b^2)

but get get that far.. here's what i have

...

1/2L{e^bt}+1/2L{e^-bt}

= 1/2[e^((s-b)t)-e^((s+b)t)]

 

[lanedance]

Homework Statement

L{sinh(bt)}

Homework Equations

sinh(bt)=(e^bt-e^-bt))

first sinh(bt)=(e^bt-e^-bt))/2

The Attempt at a Solution

so the answer says it's b/(s^2-b^2)

but get get that far.. here's what i have

...

1/2L{e^bt}+1/2L{e^-bt}

= 1/2[e^((s-b)t)-e^((s+b)t)]

not sure what you are doing here, I just went to the Tables & see
$$L(e^{-\alpha t}}) = \frac{1}{s+\alpha}$$

can you show this? and use it?

 

[myusernameis]

first sinh(bt)=(e^bt-e^-bt))/2


not sure what you are doing here, I just went to the Tables & see
$$L(e^{-\alpha t}}) = \frac{1}{s+\alpha}$$

can you show this? and use it?

yeah, we weren't supposed to use the table...