Understanding Periodic Motion Square Graphs

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SUMMARY

This discussion focuses on the graphing of periodic motion, specifically the relationship between the square of the period (T^2) and mass using a spring-mass system. Participants clarify that graphing T^2 against mass yields a linear relationship, simplifying the analysis compared to graphing T directly, which results in a parabolic curve. The key takeaway is that using a T^2-axis allows for easier slope measurement, facilitating the determination of the system's parameters.

PREREQUISITES
  • Understanding of periodic motion principles
  • Familiarity with spring-mass systems
  • Knowledge of graphing techniques in physics
  • Basic skills in data analysis and interpretation
NEXT STEPS
  • Research the mathematical derivation of the relationship between period and mass in spring systems
  • Learn about linear regression techniques for analyzing experimental data
  • Explore the concept of best-fit lines versus best-fit curves in data analysis
  • Investigate the effects of measurement errors on graphing results in physics experiments
USEFUL FOR

Students conducting experiments in physics, educators teaching concepts of periodic motion, and anyone interested in understanding the graphical representation of physical relationships in spring-mass systems.

kscribble
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I'm doing an experiment on periodic motion using a spring and a mass on the end.

My teacher wants us to graph T^2 and mass, but i don't understand we don't just graph T.

I hope someone understands what I mean :smile:
 
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Welcome to PF!

kscribble said:
I'm doing an experiment on periodic motion using a spring and a mass on the end.

My teacher wants us to graph T^2 and mass, but i don't understand we don't just graph T.

I hope someone understands what I mean :smile:

Welcome to PF! :smile:

I think your teacher means that instead of marking the t-axis 1,2,3,4,5,… at equal intervals, you mark 1,4,9,16,25,… at equal intervals.

The idea is that if you use an ordinary t-axis, you get a parabola, and you need to find the "parameter" for that parabola, which is tricky … :redface:

but with a t2-axis, you get a straight line, and all you have to do is to measure the slope of it! :smile:

(also, your measurements won't be perfect :wink:, and it's much easier to draw a best-fit line that a best-fit parabola!)
 
thank you!
i understand it now :)
 

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