graph trends

[ak21]

Hey everyone,

I was wondering if anyone knew the graph trends we should be familiar in identifying esp for PS passages. For example, I know we should be familiar with inverse proportionality graphs:

eg. X = 1/y

Are there any other ones besides this and just a linear line?

---

Members don't see this ad.

 

[plzNOCarribbean]

Hey everyone,

I was wondering if anyone knew the graph trends we should be familiar in identifying esp for PS passages. For example, I know we should be familiar with inverse proportionality graphs:

eg. X = 1/y

Are there any other ones besides this and just a linear line?

yeah, a lot of times when you modify the graph, y will be equal to the square too of x. For example, say you wanted to find the relationship between the spring constant and the velocity of the spring. set 1/2mv^2 = 1/2 Kx^2. when you re-arrange this equation to fit your dependent variable, the velocity, on one side, the other side of the equation will will be equal to the Sqroot of (k/m) times (x) where x is the displacement from the equilibirum position and K is the spring constant.

So the graph would be velocity 👍 = sqrt of K (spring constant) this graph will be "r" shaped, just like the generic graph for charging a capacitor. I don't know how to upload pics, so il just describe the graph. If you re-call, a capacitor can only store a maximum amount of charge, depending on that capacitors capacitance. As you turn a battery on, charge begins to build up on the capacitor. The charge on the capacitor INCREASES AT A DECREASING RATE, and eventually levels off.
This is similar to our velocity vs spring constant senario, which shows that the spring constant affects the velocity of the spring but at a certain point the graph levels off, indicating that as the spring constant increases (spring becomes more rigid), the velocity increases until the point where the graph begins to level off. you can think of that really as the "threshold" of how much the spring constant affects the other variable.

So, to sum up make sure you know the y= sqrroot x graph. It is "r" shaped.
also know the linear graph (y=x), and the exponential graph y= x^2, which is an upward trended graph.

 

[ak21]

thanks a lot! I think I know which graph you're talking about...it looks something like this right?

http://upload.wikimedia.org/wikipedia/commons/d/da/Capacitor_Charge_Graph.jpg

But i have a question. I don't understand why the maximum value of V would ever level off...based on the the fact that V = square root K doesn't that mean they are directly proportional? I understand the relationship shouldn't be linear because of the square root, but as long as you're increasing K shouldn't V always be increasing? Sorry if this is a stupid question! I am really bad at math lol

 

[CodeBlu]

Know everything about graphs. EVERYTHING.

There will be 2-3 questions on your PS dealing with graphs... AT LEAST.

TBR shows you lots of examples.

 

[ak21]

Yeah but TBR doesnt seem consistent in their reasoning of how/why they choose them. The same looking graph will not be the answer for two variables that share the same relationship. And in such a case their reasoning behind their first selection contradicts itself in later examples.

 

[plzNOCarribbean]

thanks a lot! I think I know which graph you're talking about...it looks something like this right?

http://upload.wikimedia.org/wikipedia/commons/d/da/Capacitor_Charge_Graph.jpg

But i have a question. I don't understand why the maximum value of V would ever level off...based on the the fact that V = square root K doesn't that mean they are directly proportional? I understand the relationship shouldn't be linear because of the square root, but as long as you're increasing K shouldn't V always be increasing? Sorry if this is a stupid question! I am really bad at math lol

Its okay I am too, I had to start from scratch in undergrad with math so that I could do well in my physics and chem classes, and I did a complete search on SDN on the same topic when trying to learn graphs

Yes, that is the right graph. And yes as long as K increases, V is increasing too BUT V is INCREASING at a DECREASING RATE. < repeat that to yourself a couple of times and look at the graph and let this settle in. The graph is leveling off although it is still increasing, it is increasing by less and less and less as K increases. This is because the spring constant can only increase V to a certain, significant extent. Any value beyond this extent is considered small, infinitesimally small, sort of like a limit.

A better example would be why a capacitor graph levels off. The reason is because when a battery is turned on, charge begins to build up on the capacitor. At some point though, so much charge has built up that it is more difficult for more charge to build up on the plates, since the plates are already occupied by a ton of charge from the conduction electrons. At this point, the graph begins to level off, and the reason that you see the graph like that is because initially, when there was no charge on the plate, the graph was increasing and a much faster rate with respect to charge building up when compared to when the graph indicated that the capacitor plate was nearly, completely occupied with charge. Hope this helps.

 

[ak21]

okay...so whenever u have x = (sq. rt of y) the graph always levels off?

 

[plzNOCarribbean]

okay...so whenever u have x = (sq. rt of y) the graph always levels off?

technically, its y= sq. root of x but either way works. When the relationship is one variable is equal to the sq root of the other you get an r shaped graph. Also, on question, make sure to look at BOTH AXES.

 

[Flamen04]

Never hurts to know what these graphs look like:

y=x
y=1/x
y=1/x^2
y=e^x
y=log x
y = sq. rt. x