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

In summary: Then you can directly read off the result from the table.In summary, the person is new to the forum and needs help with finding the Laplace transform of sin(2t). They can use the formula to get the answer, but they are struggling with understanding the steps. They are asking for assistance and someone suggests using Euler's formula to simplify the integration.
  • #1
cbird7
2
0
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
 
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  • #2
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.
 
  • #3
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)
 
  • #4
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

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

Then what?
 
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  • #5
cbird7 said:
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.
 
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Related to How Do You Derive the Laplace Transform of sin(2t)?

1. What is the Laplace Transform of sin(2t)?

The Laplace Transform of sin(2t) is equal to 2/(s^2 + 4), where s represents the complex variable.

2. How is the Laplace Transform of sin(2t) derived?

The Laplace Transform of sin(2t) is derived using the definition of Laplace Transform and the trigonometric identity sin(2t) = 2sin(t)cos(t). This results in the Laplace Transform of 2sin(t)cos(t), which can be further simplified to 2/(s^2 + 4).

3. What is the significance of the Laplace Transform of sin(2t)?

The Laplace Transform of sin(2t) is used in various applications of engineering and physics, particularly in systems that involve oscillatory motion. It allows for the representation of a time-domain function in the frequency domain, making it easier to analyze and solve problems involving differential equations.

4. Can the Laplace Transform of sin(2t) be used for other trigonometric functions?

Yes, the Laplace Transform can be applied to other trigonometric functions as well. The general rule is that the Laplace Transform of asin(bt) is equal to a/(s^2 + b^2), where a and b are constants.

5. How is the Laplace Transform of sin(2t) related to the Fourier Transform?

The Laplace Transform of sin(2t) is a special case of the Fourier Transform, where the frequency is equal to 2. The Fourier Transform is a special case of the Laplace Transform, where the variable s is set to jw, where w is the angular frequency. Therefore, the Laplace Transform of sin(2t) can be obtained from the Fourier Transform by setting w=2.

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