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    I did an experiment measuring the amplitude of swing of an object in simple harmonic motion with time. I have drawn a graph of amplitude against time, but I need to prove this is an exponential decay graph. Are there two variables i could plot that should give a straight line graph if my experiment follows the expontial decay law?
    The half lifes from my first graph aren't very good, so i need a graph that doesn't rely on me attempting to draw a curve. :p:
    Thanks.
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    If amplitude is experiencing exponential decay with respect to time then the equation of the line will be...

    A = (A.MAX) x (e^ -(k x t))

    Therefore...

    k = -(ln(A/A.MAX))/t

    to show that its exponential decay, k must be approx. constant.

    use about 5 - 10 values of A & time and see if k is roughly the same.

    EDIT: A = Amplitude at time, t
    A.MAX = Maximum amplitude of motion
    t = time

    Or if your intent on using a graph...

    A = (A.MAX) x (e^ -(k x t))
    ln A = - kt + ln(A.MAX)

    look familiar...?

    y = mx + c [y=lnA, m=-k, x=t & c=ln(A.MAX)]

    So you'll have to plot values of time against lnA at that time. If the resultant curve shape is straight, you've got yourself an exponential decay relationship between A & t.

    Hope that makes some sense.
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    plot a graph of ln A against no. of swings. (ln = natural log)

    for an exponential decay this will be a straight like with a negative gradient equal to -K where K is the decay constant

    the "half life" of the decay should also be constant and equal to ln 2 / K
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    ok, that makes sense.
    Thanks so much for your help!
 
 
 

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