Investigating Mass & Period Relationship: Slope Meaning?

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The discussion focuses on a lab experiment exploring the relationship between mass and the period of oscillation in simple harmonic motion. Participants conducted trials by adding masses to an air cart and measuring the period, ultimately graphing mass against the square of the period (T^2). The main inquiry is about the meaning of the slope of this graph, with initial thoughts suggesting it could relate to the spring constant. However, further analysis indicates that the slope may represent a different physical quantity, prompting a suggestion to rearrange the period equation for clarity. Understanding the slope's significance is crucial for interpreting the results of the experiment.
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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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