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Im not sure if this is a math question or a su question.

The experiment was relating the period of one "bounce" when you hang a weight on a spring and let it bounce.

I have this data here, one being mass and one being time.

The time is an average of 5 trials, each one being and average of 20 bounces, to minimize human error.

t

0.3049s
0.3982s
0.4838s
0.5572s
0.6219s
0.6804s
0.7362s
0.7811s
0.8328s
0.869s

The mass is the mass that was used in each trial (they aren't going up in exact differences because each weight has a slight difference, nothing is perfect in the real world)

m

50.59g
100.43g
150.25g
200.19g
250.89g
301.16g
351.28g
400.79g
450.43g
499.71g

My problem is that I need to find the relationship between them, I know m = (k/4PI^2)*T^2 so I can work out k like that but we need to graph it.

I can assume that the relationship is a sqrt relation, not sure on that one. But it appears to be the reverse of a square. Should it be 1/x^2 then?

Either way my problem is still present, I have tried 1/x, 1/x^2, sqrt, x^2, none of them produce a straight line.

The problem for SU is that when I go to graph the data on Excel I set the y axis data (which is the weights) and then when I go to set the x axis (which is the time) it just replaces the y axis with what I want to be the x axis, this is only happening when I have the sqrt of "m" as the y axis and I try to set the x axis as the time.

The problem of math is that, am I even using the right thing? To get a straight line it would need to be x = y^1/2 right? I thought I was doing the right thing, it is what we were told to do. I'm just not getting anything that looks right.

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2 Answers

up vote 3 down vote accepted

As Trudbert already pointed out, you'll need to plot T^2 if you want a straight line. To get Excel to behave properly, you'll need your data laid out appropriately, and you'll need to do everything in an order that keeps Excel from making bad decisions for you.

Time v. Mass

  1. Lay out your data with your X values (Time) and Y values (Mass) in two columns, with an open column between them (e.g. columns A and C).
  2. In the open column (e.g. column B), add a formula to calculate T^2 (e.g. =A2^2).
  3. Select an open cell (not one of your data cells) and Insert>Chart(Scatter). This will create a completely blank chart-no Excel defaults to deal with.
  4. Right click and choose Select Data.
  5. Add a Series, using your T^2 (e.g. column B) for your X values and your M column (e.g. column C) for your Y values.
  6. Format to suit.

Note, if you choose a different chart type (e.g. line) or if you let Excel try and create your series for you automatically, you'll be fighting Excel for everything. By going through the extra steps above, you'll save yourself a lot of trouble getting your chart to look correct.

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You need to plot m vs. T^2 that will give you a straight line which slope should be around k/4Pi^2. That is because your equation for m is already the equation for a straight line y=ax with y being m, a=k/4Pi^2 and x=T^2 so if you plot m vs. T^2 or vice versa you get a straight line with slop a or 1/a from which you can extract k.

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