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# Time to Half Watch

1. 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?
2. 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 ...
3. 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.
4. 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.
5. (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).
6. 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
7. Ok.

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

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Updated: March 28, 2013
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