SHM, Determing Spring Constant from Period^2 vs. Mass

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SUMMARY

The discussion focuses on determining the spring constant (k) from a graph of Period squared (T^2) versus Mass (m) using the principles of simple harmonic motion. The relationship is defined by the equation T = 2π√(m/k), which can be rearranged to T^2 = (4π^2/k) * m. The slope of the linear fit, 5.237, directly correlates to the term (4π^2/k), allowing for the calculation of k as k = 4π^2/5.237. This method provides a clear and effective approach to finding the spring constant from experimental data.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with linear regression and slope interpretation
  • Knowledge of the equation T = 2π√(m/k)
  • Basic graphing skills for plotting T^2 vs. Mass
NEXT STEPS
  • Calculate the spring constant (k) using k = 4π^2/5.237
  • Explore the effects of varying mass on the period of a spring system
  • Learn about the implications of damping on simple harmonic motion
  • Investigate other methods for measuring spring constants, such as static methods
USEFUL FOR

Students in physics, educators teaching mechanics, and researchers conducting experiments involving oscillatory motion will benefit from this discussion.

nmacholl
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Help!

I'm trying to find the spring constant (k) of a spring using simple harmonic motion. I have a graph of Period^2 vs. Mass.

Knowing that T=2*[tex]\pi[/tex]*[tex]\sqrt{m/k}[/tex]

How would one find k from the slope of this graph?
My linear fit yields: y=5.237x+0.003
5.237 being my slope
 
Physics news on Phys.org
HINT: Using what you know can you get an Equations for T^2 in terms of mass? If so, the slope of that equation is 5.237.
 

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