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    hey dudes long time no speak,
    matter of urgency for uni work 2moro - any help greatly appreciated.
    1. whats the laplace of
    (e^(-pie s)) / s^2 + 4
    its to do with the heaviside function...

    2. whats the laplace of f(t) = [H(t - 1) - H(t - 2)]t ?

    3. find x(t) when : (s - 2) x(t) - s y(t) = -0.5
    and s x(t) + (s - 2) y(t) = (4 + 3s^2) / 2s^s
    (differential equations)

    as i said any help is definitely needed
    thanks
    x o x
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    You sure you dont want the inverse for 1)?
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    (Original post by JamesF)
    You sure you dont want the inverse for 1)?
    probably! i need anything, im a big ball of confusion! do u think u can help me?

    x o x
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    Possibly ...gimme a few minutes
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    (Original post by JamesF)
    Possibly ...gimme a few minutes
    aww thanks!! good luck!!
    x o x
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    Right, i'll have a go...
    Do you know the result:
    e^-(cs).f(s) = L{ H(t-c).F(t-c) } ??

    Taking c = pi, and f(s) = 1/(s^2 + 4), you get the answer for the first question.
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    2) L{ H(t-c) } = integral from 0 to infinity of e^(-st).H(t-c) dt

    But H(t-c) is 0 until t > c, so you can just change the limits from 0 to c, and get rid of the heavyside function, leaving
    integral from c to infinity of e^(-st) dt = 1/s * e^(-cs)

    So the transform of f(t) = H(t-1) + H(t-2) is just e^(-s) + 0.5e^(-2s)

    Then L{ t.f(t) } = -f '(s), so the answer to the second question is e^(-s) + e^(-2s)

    I think
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    For the third, i think you just eliminate x(t) to find y(t) and then go back, eliminate y(t) to find x(t).
    Im not sure what x(t) and y(t) are (possibly x(t) = L{x} ? would make sense), so i dont know how the differential equations come in.
 
 
 
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Updated: November 9, 2004

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