Question

We are doing a lab on pendulums, which I understand fully. BUT, I am unsure what the question is asking me to do:
[On GraphicAnalysis] The resulting graph is a half-parabola around the x axis. It means that the variable on the y axis is directly related to the square root of the variable on the x axis.

1. Express this relationship using the variables you analyzed instead of the generic "y" and "x."

2. Remember that the square root of x can be written as x1/2. If the generic equation is y = kx1/2, write the specific equation suggested by the actual variables in this graphical data.

Answer 1

the graph is presumably period on the y axis and length of pendulum on the x
the generic is y=kx^1/2

so period = kl^1/2

Calculate k from the graph, and substitute above...

Answer 2

Yes, sorry, forgot to clarify the axis.
How did you go from the generic equation to just \[k^{1/2}\]

Answer 3

Or maybe a better question:
What exactly does k represent?

Answer 4

it is k l^1/2 (not k^1/2) : l = length

The question tells you the relationship :"It means that the variable on the y axis is directly related to the square root of the variable on the x axis"

directly related means that it is related by a constant ,but depends on sqrt(L)

from the graph you can find a value for the constant.

The actual value will mdepend on your experimental results

The theoretical formula is \[T= 2\pi \sqrt{\frac{ l }{ g}}\]

So your constant should turn out to be close to \[2\pi \sqrt{\frac{ 1 }{ g}}\]

Answer 5

Okay, so looking back on the question, the "variable you analyzed" would be the period vs length of pendulum, right?
So y=period
x=pendulum length

Also using the question, sqrt(L) refers to the pendulum length?

Answer 6

But does k represent the constant?

Answer 7

yes (I used L rather than l for ease of reading in this forum)

k is the constant - and the formula gives you the theoretical value. The value you get will depend on your experimental errors.

Answer 8

if you take your data and plot period agains sqrt(L) tehnyour graph should be a straight line.

The SLOPE of that line will give you the value of k

Answer 9

When i plot my data, it turns into the half-parabola as mentioned in the question?

Answer 10

if your experimental method is good

Answer 11

I did it using an online simulation, so it's pretty accurate, i think

Answer 12

remember - it is the experiment that verifies the theory - not the other way round!

Answer 13

i think i'm really confused because 1. this is an online class, and 2. i can't seem to find any formulas, or anything explaining what's going on previously

Answer 14

do you have data relating period against length?

If so - plot it
(pen and paper is good!)

Answer 15

Do you understand that this represents data obtained by changing the length of a pendulum and measuring the time it takes to swing 1 cycle?

Answer 16

The data has been plotted for you and the software shows you the best values that it derives for \[Y=A X^{B}\]

The best values (from the picture)\[Y=2.388X ^{0.4975}\]

Answer 17

Yes, I understand what the data represents, since I gathered it... According to the lesson, this is period vs length?
that's why i was unsure if i could use the "power" equation they gave as y=ax^b, because it didn't match up with the "k" values, discussing square roots.

Answer 18

& also, i don't understand the difference between the first and second question, besides perhaps the formulas...

Answer 19

a is the constant in the equation above.

k is just another notation for a given constant.

http://en.wikipedia.org/wiki/Pendulum

I'm off for an hour or so

Answer 20

Okay, I think I get it now. Or at least have some idea of what's going on haha. Thank you so much!