Investigating Mass & Period Relationship: Slope Meaning?

[MJC8719]

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

 

[Kurdt]

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.

 

[m2003]

Hello,

Thank you for sharing your experiment and question. The relationship between mass and period in simple harmonic motion is a well-known one, and it is represented by the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. When graphed, this relationship should result in a straight line with a positive slope.

The slope of this line represents the square root of the spring constant divided by 2π. In other words, it represents the relationship between the mass and the force required to produce simple harmonic motion. This means that the steeper the slope, the higher the spring constant and the stronger the force needed to produce the same period of oscillation.

I hope this helps clarify the meaning of the slope in your experiment. Keep up the good work in your scientific investigations!