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Math Help - Laplace Transformation question

  1. #1
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    Laplace Transformation question

    Hi, i do not know where to post this so i just figured i leave this where there are most people viewing. I need help doing question 4 only. Thanks!!
    Laplace Transformation question-untitled.png
    Laplace Transformation question-untitled1.png
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  2. #2
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    Re: Laplace Transformation question

    The steady state part can be expressed in the form

    v_{steady}=A\sin (\omega t + \alpha) = A\sin \omega t \cos \alpha + A \cos \omega t \sin \alpha,

    where A is the amplitude.

    Equate coefficients of \sin \omega t and \cos \omega t with the corresponding expressions in your formula for v_{steady}, and eliminate the \cos \alpha \text{ and } \ sin \alpha by squaring and adding.
    Thanks from joshua111
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  3. #3
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    Re: Laplace Transformation question

    Quote Originally Posted by BobP View Post
    The steady state part can be expressed in the form

    v_{steady}=A\sin (\omega t + \alpha) = A\sin \omega t \cos \alpha + A \cos \omega t \sin \alpha,

    where A is the amplitude.

    Equate coefficients of \sin \omega t and \cos \omega t with the corresponding expressions in your formula for v_{steady}, and eliminate the \cos \alpha \text{ and } \ sin \alpha by squaring and adding.
    Hi,
    I'm really bad at this but if you have the time, do you mind showing how to get to the final answer?
    Thanks!
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  4. #4
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    Re: Laplace Transformation question

    If A\sin \theta = p \text{ and } A\cos \theta = q,
    then ,squaring and adding,
    A^{2}(\sin ^{2}\theta + \cos ^{2}\theta) = p^{2} + q^{2},
    so
    A = \sqrt {p^{2} + q^{2}.
    And sorry, but I know absolutely nothing about the filters mentioned in the question.
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  5. #5
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    Re: Laplace Transformation question

    Quote Originally Posted by BobP View Post
    If A\sin \theta = p \text{ and } A\cos \theta = q,
    then ,squaring and adding,
    A^{2}(\sin ^{2}\theta + \cos ^{2}\theta) = p^{2} + q^{2},
    so
    A = \sqrt {p^{2} + q^{2}.
    And sorry, but I know absolutely nothing about the filters mentioned in the question.
    Sorry, but i'm a bit confused. How did you derive the Vsteady equation in post #2.
    And in post #4 wouldn't A=((p^2+q^2)/(Sin^2 theta +cos^2 theta))^(1/2)
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  6. #6
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    Re: Laplace Transformation question

    I didn't derive anything in post 2, I simply stated what should (at your stage) be a well-known trig identity, and what allows the the expression for v_{steady} given in the question to be written in an alternative form.

    Another trig identity, with which you should be familiar, is used later. \cos^{2}\theta+\sin^{2}\theta=1.
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