Rearranging Equations to y= mx + b

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To graph the given data in Excel and establish a linear relationship, it is necessary to identify the independent (x) and dependent (y) variables correctly. The equation T=2π√(lcosα/g) can be rearranged to T² = 4π²cosα/g, but this results in a quadratic relationship, complicating the linear fit. The discussion highlights confusion regarding the variables, with T being the dependent variable and the angle as the independent variable. Suggestions include finding a linear fit over a small interval of x, as the original equation does not lend itself to a straightforward linear transformation. The conversation emphasizes the challenge of transforming the equation while acknowledging the need for accurate data for proper analysis.
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Homework Statement


Graph the following charts on excel so you have a linear relationship.
Determine your x and y variables before graphing, you may have to rearrange and even recalculate some of the variables.

Angle Period (s)
0 0.95
10 0.94
20 0.97
30 1.00
40 1.03
50 1.09
60 1.14
NOTE: TEACHER SAID THAT SHE GAVE THE WRONG NUMBERS, THESE WONT WORK, JUST GIVING THEM INCASE ANYONE ASKS.

Homework Equations



T=2π√(lcosα/g)
Fixed l of 1.0 m
What is g?

The Attempt at a Solution



Firstly, I have to get rid of the square root

T^2 = 4π^2cosx/g
I removed the l since it is equal to 1 and is a constant

The problem is here already. What can I do to make it a linear function. The moment i squared the T it became a quadratic/ arc.

I KNOW it isn't much, but i am struggling for so long and can't seem to get anywhere. Sorry about that guys.
 
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Ranjan1995 said:

Homework Statement


Graph the following charts on excel so you have a linear relationship.
Determine your x and y variables before graphing, you may have to rearrange and even recalculate some of the variables.

Angle Period (s)
0 0.95
10 0.94
20 0.97
30 1.00
40 1.03
50 1.09
60 1.14
NOTE: TEACHER SAID THAT SHE GAVE THE WRONG NUMBERS, THESE WONT WORK, JUST GIVING THEM INCASE ANYONE ASKS.

Homework Equations



T=2π√(lcosα/g)
Fixed l of 1.0 m
What is g?



The Attempt at a Solution



Firstly, I have to get rid of the square root

T^2 = 4πcosx/g
I removed the l since it is equal to 1 and is a constant

The problem is here already. What can I do to make it a linear function. The moment i squared the T it became a quadratic/ arc.

I KNOW it isn't much, but i am struggling for so long and can't seem to get anywhere. Sorry about that guys.

In the beginning of your problem statement, you mention x and y. But then in the equation there is no "y". Is x the independent variable in the equation? If so, what is the dependent variable?
 
T is the dependent variable
 
So you mean x and T rather than x and y?
 
Yes, sorry.
 
Well I could be wrong, but I don't think you can fit a linear equation to the T = SQRT(cos(x)) equation that you are given. Are you maybe supposed to find the best linear fit across some small interval of x?
 

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