Proportinality graphs of data set

[TheLegace]

Homework Statement

I am given dataset for period of a pendulum.
Length(cm) - 20 , 40 , 60 , 80 , 100
Period(1 cycle)- .89 , 1.26 , 1.55 , 1.79 , 2.00

Calculated
Frequency(1/Period) 1.12,0.79,0.65,0.56,0.50
Period^2 0.79,1.59,2.40,3.20,4.00

Homework Equations

I am suppose to create porportionality graphs, for data originally from the Length vs. Period data, the first graph provides a power relationship. As I go further to describe 1/Period, or known as the frequency I get an inverse relationship, now I need to make a third graph to create a linear relationship. My question is when modifying x-values to create porportionality graphs, do we only modify original data(x-values)? Since I have worked out Period^2 it does provide me with a linear relationship, now I just need to work on a porportionality statement. Would someone be able to confirm my answers. Also I need to relate the slope of the linear relationship to the frequency, I have no idea what that could be, but I am going to keep thinking about it.

Thank You Very Much

The Attempt at a Solution

Would this be the porportionality statement?
Also I couldn't find the symbol for portionality, so that's the closest thing I could find.
LengthфPeriod^2

 

[anathema]

Dear fellow scientist,

Thank you for sharing your data and progress on your assignment. It seems like you are on the right track in creating proportionality graphs for your data. To answer your question, when modifying x-values to create proportionality graphs, you should only modify the original data (x-values) and keep the dependent variable (y-values) the same. This allows for a clear comparison between the two variables.

Your proportionality statement, "LengthфPeriod^2", is correct. The symbol for proportionality is ∝, where A ∝ B means that A is directly proportional to B. In your case, as the length increases, the period squared also increases.

To relate the slope of the linear relationship to the frequency, you can use the equation for simple harmonic motion: T=2π√(m/k), where T is the period, m is the mass, and k is the spring constant. In this case, the slope of the linear relationship would be related to the frequency by the equation f=1/T. I hope this helps in your further exploration of your data. Keep up the good work!

 

[Moetasim]

Thank you for sharing your data set and questions. It seems like you have a good understanding of the concept of proportionality and how it relates to your data. To answer your question, when creating proportionality graphs, you only modify the original data values (x-values) and not any calculated values. This is because the original data represents the independent variable and the calculated values represent the dependent variable.

Your proportionality statement, using the symbol "ф" for proportionality, is correct: LengthфPeriod^2. This means that the length of the pendulum is directly proportional to the square of its period.

To relate the slope of the linear relationship to the frequency, you can use the formula for the slope of a line, which is rise/run or (change in y)/(change in x). In this case, the y-values represent the frequency and the x-values represent the period^2. So the slope would be (change in frequency)/(change in period^2). This value would be constant for all points on the line and can be used to compare the frequencies at different period^2 values.

I hope this helps and good luck with your proportionality graphs!