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Math Help - Solving exponential simultaneous equations

  1. #1
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    Solving exponential simultaneous equations

    The actual problem shows a graph however I can state all the information. The graph is of a sinusiodal waveform where the amplitude is decaying exponentially. The formula for the graph is given by the equation:

    T = Ae^-Ktsin(wt + )

    The question is to find A,K,w and

    Being quite confident in sinusoidal waveforms I can tell you that:

    w = 40 x pi or 125.66 (whichever tickles your fancy)
    = -1.885

    However im stuck with the A and K.

    Assuming that the maximum peaks occur when sin(wt + ) = 1 then:

    0.23 = Ae^-K0.0275

    0.08 = Ae^-K0.0775

    I now have 2 points to solve simultaneously for A and K.

    Heres my attempt:

    0.23/0.08 = Ae^-K0.0275/Ae^-K0.0775

    2.875 = e^-K0.5

    K = (1/0.5) x ln(2.875) = 2.1121


    When you plug this back into the two equations however you get two different answers for A and A is supposed to be a constant!! Can anyone see where im going wrong here?

    Thanks in advance for any help.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    0.23/0.08 = Ae^-K0.0275/Ae^-K0.0775

    2.875 = e^K0.05

    K = (1/0.05) x ln(2.875) = 21.121
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  3. #3
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    oops LOL. Thats typical me that is. Do all the hard work then miss out a zero or put in the wrong sign convention. lol. cheers.
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