/sci/ - Science & Math

[Anonymous No.1926225]

>oh god how do I cartesian planes I don't even

One question on an assignment I'm currently working on asks that I "plot and replot the data observed until a straight line is obtained". I've never had to do this before. how do I go about this?

If it helps, I'm trying to determine proportionality statements.

[Anonymous No.1926247]

>>1926225

what's the data? like what physical observables are we talking about, speed, acceleration, force, current etc?

[Anonymous No.1926252]

>>1926247
It's three different graphs:
- Frequency over force
- Frequency over mass
- Frequency over radius

I fail to see how to determine the proportionality statements from my graphs, though. The only graph with a positive slope is the first one.

[Anonymous No.1926263]

>>1926252

i don't think i'm quite getting you. when you say you don't know how to determine proportionality from your graph, what do you mean?

if you're plotting frequency vs. something, and if the graph is linear (or you can do a linear fit on the data), then the slope is the proportionality.

[Anonymous No.1926303]

>>1926263
According to my solutions manual, the proportionaloty of the first graph, for example, is Freq. ∝ sqrt(Force).

I don't see how to get this, as my graph isn't linear.

[Anonymous No.1926309]

>>1926303

oh there's your problem

your relationship isn't linear, so of course if you just plot frequency vs force (i assume you're talking about a spring-mass system here), you will never get a straight line.

what you need to do in these cases where Y = X^n is to do LOG PLOTS

[Anonymous No.1926311]

OP here, these are my graphs.
I just applied a linear trend line to them.

[Anonymous No.1926315]

>>1926311
lolnoimagefile

[Anonymous No.1926316]

>>1926303
The problem is to MAKE it linear. Notice how they had a sqrt? Those sort of tricks. So to make say, y=x^2 as graphed against the x and y axes into a line, you would change the axes to like, sqrt(y) and x. If you were to graph y=x^2 on those axes, you would get a line.

[Anonymous No.1926321]

>>1926309

i.e, instead of plotting freq vs. force, plot

log(freq) vs. log(force)
where log can be base 10 (lg) or base e (ln)

goes like this:

log(freq) ∝ log[(force)^1/2]

==> log(freq) ∝ (1/2)*log(force)

so the LOG plot will be linear, and the slope is going to be 1/2,

[Anonymous No.1926324]

>>1926316

log plots are infinitely superior. they give you the exact value of the exponent from the slope of your linear fit, without you knowing beforehand what the exponent actually is.

[Anonymous No.1926325]

>>1926316
>>1926321
Ah, now this is making more sense.
I'll try both of these.

[Anonymous No.1926331]

>>1926325

ignore the other one - it involves trial and error or you cheating (i.e. knowing what the power is beforehand). just plot the log graph and you'll see.

[Anonymous No.1926334]

>>1926324
Yeah. I just fucking hate logs.

[Anonymous No.1926352]

>>1926331
I tried taking the logs of my values, both x and y axes, and I still can't get a linear graph.

Here's my table of values for reference.

[Anonymous No.1926357]

>>1926334

logs are nothing more than operations which are of an order above multiplication/division, just like multiplication/division are of an order above addition/subtraction. your hatred towards logs kind of shows your mathematical maturity. remember back in the old days when you hated divisions? it's a phase. it will pass.

[Anonymous No.1926363]

>>1926357
Oh no, I'm perfectly capable of doing logs, and they are undeniably useful. I just dislike hassling with them.

[Anonymous No.1926365]

>>1926352

what's stopper mass and hanging mass? you sure you don't have to add them together?

[Anonymous No.1926374]

>>1926352

problem is, you're varying more than one parameters.

to plot frequency vs. something, or the log version of that, and get a meaningful answer, you need to vary only that something and nothing else, otherwise you won't get anything meaningful.

so in your case i think maybe you should've done something different in the experiment, like varying force first while keeping all other things constant, get a bunch of data points, then vary something else

[Anonymous No.1926380]

>>1926365
Stopper mass is attached to one end of a string.
Hanger mass is at the other end, and provides a tension force.

>>1926374
I did vary only one parameter, I kept the others constant. The parameter varied was used to calculate the frequency, in conjunction with the cycles and other constant values.

[Anonymous No.1926384]

Also note: here are the proportionality statements right from the book.

[Anonymous No.1926388]

>>1926380

so are you saying, if you do the log plot of frequency vs. force for the first three data points, where you only varied the hanging mass, you don't get a straight line?

if that's the case, there might be something wrong with your data

[Anonymous No.1926389]

Also note: here are the proportionality statements right from the book.

[Anonymous No.1926395]

>>1926388
I tried taking the log plot of frequency/force, and it wasn't a straight line. However, I'm not sure if I did it correctly, so it could just be me.

[Anonymous No.1926406]

>>1926395

i tried, no straight line for either radius or force. that means your data is messed up

[Anonymous No.1926417]

>>1926406
Hmm, interesting.
The data followed my hypothesis though.

Maybe I could try to bluff something then, I'm not redoing the entire experiment.

[Anonymous No.1926427]

>>1926417

that's exactly what you should do

play around with the values until you get a straight line.

however, in this case it's better to not plot the log versions and go to frequency vs. x^1/2 etc. etc.

[Anonymous No.1926439]

>>1926427
I'll see what I can do.
Our labs were completed in groups, so it's not like I can rewrite every value without telling the other partners.