Rearranging Equations to y= mx + b

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Homework Help Overview

The discussion revolves around rearranging the equation for the period of a pendulum, T, in relation to the angle, α, to establish a linear relationship suitable for graphing. The original poster provides a set of angle and period data, noting that the numbers may be incorrect, and seeks guidance on how to manipulate the equation to achieve a linear form.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to eliminate the square root in the equation T=2π√(lcosα/g) to achieve a linear function. There are questions about the roles of the variables, specifically identifying which is independent and which is dependent. Some participants suggest the possibility of fitting a linear equation to a specific interval of x.

Discussion Status

The conversation is ongoing, with participants clarifying variable roles and exploring the feasibility of fitting a linear model to the provided data. There is no explicit consensus on the method to achieve linearity, but various interpretations and approaches are being considered.

Contextual Notes

There is mention of potentially incorrect data provided by the teacher, which may affect the analysis. The fixed length of the pendulum is noted, but the value of g remains a point of inquiry.

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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.
 
Last edited:
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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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