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Math Help - Find Laplace Transform

  1. #1
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    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)
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  2. #2
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    Re: Find Laplace Transform

    Quote Originally Posted by nak5120 View Post
    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
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  3. #3
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    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?
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Find Laplace Transform

    Quote Originally Posted by nak5120 View Post
    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
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