Which Axis is Correct for Plotting t² and Length in Physics Graphs?

[noname1]

I have to plot the period t² vs the length but now i am confused which goes on the x-axis and which goes to the y axis, i was wondering if someone could help me out with this issue

 

[Rajini]

Seems like length in y-axis and t² in x-axis. But what you do ? and which behavior you want to plot?
Generally fixed data goes to x-axis and dependent (i mean dependent on x-axis data) goes to y-axis..

 

[noname1]

I am trying to plot the period of a pendulum, where l is given which is the length of the cord and t² is the period squared determined by me, so i guess L goes to Y and t² goes to x?

 

[Rajini]

Yes it is up to you..But i guess you want to do some lab experiment where you want to determine experimentally the acceleration due to gravity g?..in that case you can plot cord length L (or $$\sqrt L$$) in x-axis and average t for 1 oscillation in y-axis..by plotting such graphs you can find slope, which gives the idea of g...
But i think you know slope, straight line intersecting y-axis, etc..
good luck.

 

[AC130Nav]

I am trying to plot the period of a pendulum, where l is given which is the length of the cord and t² is the period squared determined by me, so i guess L goes to Y and t² goes to x?

Wouldn't it be better to plot the displacement versus the cumulative time (x axis)? Gives a more useful sine wave.

 

[noname1]

Yes it is up to you..But i guess you want to do some lab experiment where you want to determine experimentally the acceleration due to gravity g?..in that case you can plot cord length L (or $$\sqrt L$$) in x-axis and average t for 1 oscillation in y-axis..by plotting such graphs you can find slope, which gives the idea of g...
But i think you know slope, straight line intersecting y-axis, etc..
good luck.

Yes i am doing this for a lab project, i am trying to obtain g by the slope and the data that gives me close to 9.8 is L for y and t² for x but i am just not sure if those are the appropriate places

 

[Rajini]

Good. then just plot $$\sqrt L$$ in x-axis and t in y-axis. Now find the slope (better after fitting the line with a straight line).
Now you know the pendulum relation..compare this relation with slope and obtain the g.
for details:
http://www.8886.co.uk/pendex1.htm

 

[RoyalCat]

Wouldn't it be better to plot the displacement versus the cumulative time (x axis)? Gives a more useful sine wave.

A sine wave is pretty much useless. You cannot take the slope of a sine wave, all you can do is say, well, the motion is periodic, and that's nothing you didn't already know.

Other than getting ideas for the form of a function, you should always plot graphs which you think will be linear.

For instance, let's say we have a dependent variable, y, and an independent variable, x. We don't have a theory telling us what y as a function of x is.

What we should do is first look at the graph of y as a function of x, to get an idea of what the functional form is. Suppose we see that the graph reminds us of a high degree polynomial.

Let's assume then that $$y=kx^n$$ and try and get the full functional form from a graph, given some values $$(x,y)$$

How would we go about this? We would linearize the graph, since without great computing power, we don't really have a way of distinguishing one polynomial plot from another.

What we can do, however, is look at the equation $$y=kx^n$$ and -linearize- it, so that we have a graph we can extract data from (Plotting a trend line and computing the slope and intercept, which we can then relate to our unknown constants, which is something we are fully capable of).

One way of determining k and n, would be to look at the following relation:
$$y=kx^n$$
which implies:
$$\ln{y}=\ln{kx^n}$$

$$\ln{y}=\ln{k}+n\ln{x}$$
When plotting $$\ln{y}$$ as a function of $$\ln{x}$$ we would expect a linear graph whose slope is $$n$$ and whose intercept is $$\ln{k}$$

From the y as a function of x graph, we found the form of the function (Which you would usually know from a separate source anyway) and from the linear graph, we managed to extract numerical information from the data.

Since for the most part, slope data is more accurate than intercept data, knowing $$n$$ from the logarithmic graph, we can then construct a graph of $$y$$ as a function of $$x^n$$, and this graph too, we expect to be linear, with a slope equal to $$k$$ and an intercept of 0.

Which one goes on the horizontal axis, and which one on the vertical axis is simply a matter of convention where the independent variable (What you change, knowing exactly the change you've made) goes on the horizontal axis and the dependent variable (What you measure after making the change to the system) goes on the vertical axis. In your experiment you, the one conducting the experiment, changed the length of the wire of the pendulum, and what you had measured was the period.

So if you wish to follow the convention, you should plot the period squared on the vertical axis, and the length of the wire on the horizontal axis.

 

[noname1]

Now i have a question that says, from the slope, determine the acceleration of gravity G, but isn't g just the slope m?

Or can i solve g this way

g = (4pi^2)/slope

 

[Rajini]

Now i have a question that says, from the slope, determine the acceleration of gravity G, but isn't g just the slope m?

Or can i solve g this way

g = (4pi^2)/slope

Yes you can.
If t² in y-axis and L in x-axis, then, $$g=4\pi^2/(\rm slope)$$.
or if you want to play with then do like the following if you are interested:
make another plot t² in x-axis and L in y-axis and here i guess $$g=4\pi^2\times(\rm slope)$$.