How Do You Derive the Laplace Transform of sin(2t)?

[cbird7]

im new to this forum. i really need help with the steps to solve the Laplace of sin(2t). i can put it in the formula to get the answer but I am having problems getting the steps which is what i need to follow and understand it better. if anyone can please help me with the steps it would be much appreciated. thanks

 

[vela]

It's not clear what you're asking. What do you mean when you say you want to "solve the Laplace of sin(2t)"? Do you mean you want to find the Laplace transform of sin 2t by using the integral? If so, post what you've done so far so we can see where you're getting stuck.

 

[cbird7]

yea that's exactly what i want. I am getting stuck on the integration by parts. i can use the general steps to get through but I am confused on how to go to the next step.

the farthest i got was:
=(-1/s)e^-st*sin(2t)+(1/s^2)e^-st-(cos(t)/2)-(1/s^2)sin(2t)

 

[vela]

What you wrote doesn't make sense to me. I'm guessing you left some stuff out. You should learn LaTeX so you can express the integrals clearly. It's pretty straightforward.

https://www.physicsforums.com/showthread.php?t=386951

So you started with

L[\sin 2t] = \int_0^\infty (\sin 2t)e^{-st}\,dt

Then what?

 

[klondike]

im new to this forum. i really need help with the steps to solve the Laplace of sin(2t). i can put it in the formula to get the answer but I am having problems getting the steps which is what i need to follow and understand it better. if anyone can please help me with the steps it would be much appreciated. thanks

Are you saying you can find the LT of sin(2t) by looking up from the table of Laplace Transforms but don't know how to derive it from the integral?

You can integrate by parts but perhaps the easiest way is to express sin(2t) in form of complex exponential using the Euler's formula.