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    Hi,



    Traditionally time to half can be calculated by viewing exponential decay on a graph and calculating the point at which the point is half the original amplitude (as seen in graph 1).

    However, how do you calculate a time to half if the graph looks like graph 2?


    Would/Could it literally be when the value is of half? So in Graph 2 if the peak is 10, and (marked green X on graph) is value 5... could the time taken to reach that point be used as the Time To Half or not????


    Anyone chip in their thoughts on this please?
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    Draw a graph showing the max amplitude of each peak against time. Join with a smooth curve. Look at time to halve amplitude.

    You've marked a point where DISPLACEMENT halves.
    This isn't the point youre looking for ...
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    The time where amplitude halves is exactly at the point where displacement halves because the displacement IS the amplitude.

    My point is in Graph 2 it is damped, and therefore the graph does as it shows and therefore there are no peaks to draw apart from what is shown. Meaning the next peak in graph 2 is at the very bottom (near 0) and obviously at that point the value has more than halved (possibly 90% reduction).


    So my point was, in graph 2 (I know how to do it for graph 1)... would the time to halve literally be when on graph 2 the value reaches 5? (in which case it would be a very fast time to half?)

    Hope that makes sense.
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    I dont think so - in graph2 - the Amplitude at the point where the displacement is 5 isnt 5! You dont know what the amplitude is at that time.

    You only have 3 points where you can meaure the amplitude so youre not going to get very accurate results. But you should sketch a graph of amplitude against time. Draw a curve through the 3 points and look at the time for the amplitude to halve.
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    (Original post by teachercol)
    I dont think so - in graph2 - the Amplitude at the point where the displacement is 5 isnt 5! You dont know what the amplitude is at that time.

    You only have 3 points where you can meaure the amplitude so youre not going to get very accurate results. But you should sketch a graph of amplitude against time. Draw a curve through the 3 points and look at the time for the amplitude to halve.
    Could you draw me what you mean?

    How can I sketch amplitude against time when that is what I already have drawn?



    I assume you mean the three points (black +'s) which I have marked above? If so it would produce exactly the same plot.

    The next "amplitude" to use has a value which is way beyond half the value of the initial amplitude (more like 90% less than the initial value).
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    Your graph is displacement against time.

    Take the positive values of those three points and you have three values of amplitude.

    Draw an exponential through them
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    Ok.

    Also any idea if you can calculate the period of an exponential decay such as the one seen in Graph 2?
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    You need to look at the points where the graph crosses the axis and get some sort of average.
 
 
 
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