Investigating Mass & Period Relationship: Slope Meaning?

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SUMMARY

The discussion centers on the relationship between mass and the period of oscillation in a simple harmonic motion experiment using an air cart and springs. The participants graphed mass (m) against the square of the period (T²) and sought to understand the significance of the slope of this linear relationship. The relevant equation is T = 2π√(m/k), which can be rearranged to show that the slope of the graph represents 4π²/k, where k is the spring constant. This confirms that the slope is inversely proportional to the spring constant.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with the equation T = 2π√(m/k)
  • Basic graphing skills, particularly linear relationships
  • Knowledge of spring constants and their role in oscillatory systems
NEXT STEPS
  • Research the derivation of the period equation T = 2π√(m/k)
  • Learn how to experimentally determine the spring constant (k)
  • Explore the implications of mass on oscillation frequency
  • Study the relationship between energy and oscillations in harmonic motion
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Students and educators in physics, particularly those focusing on mechanics and oscillatory motion, as well as researchers interested in experimental physics methodologies.

MJC8719
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Hi,

We have been working on a lab that dealt with oscillations and simple harmonic motion. We attached two springs to an air cart, placed it on an air track, and released a distance of 10cm from the equilibirum point. To investigate the relationship between mass and the period, we added 50 g masses to the cart and performed various trials and timed the period.

We then were instructed to graph the m vs T^2 with m being the total mass and T^2 being the time of the period squared. My question is, what does the slope of this line represent. The line increases linerly, and i believe that the relevant equation is
T of period = 2pi SwRt(m/k)...or is it k/m...i can't remember right now as I am at work...

but anyways...what could the slope of the line represent...i first thought it might be the spring constant...but I do not believe that is correct anymore...

any ideas would be greatly appreciated
 
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Remember the equation of a straight line y = ax + b, where m is the gradient or the slope. If y = m and x = T2 then what is a?

Hint: Try rearranging your period equation.
 

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