Finding the variable S using the intercept in simple harmonic motion of spring.

[Finaid]

In an experiment to determine g using simple harmonic motion using a harmonic oscillator, a motion sensor and data logging equipment. I have all the variables but I can't figure out how to get S in the following equation:
T^2 = ((4pi^2)/k)M + ((4pi^2)/k)S ...(1)

I have a graph of T^2 (the period) vs Mass of the hanging load.
The slope is 1.863 +/- 0.016 s^2 kg^-1
The intercept is 0.006 +/- 0.001
From the above equation: k= 4pi^2/slope
=> k=21.19 +/- 0.18 kg s^-2

I also have a graph of x' (extension of spring) vs. Mass of load.
The slope is 0.421 +/- 0.034 m kg^-1
The intercept is -0.009 +/- 0.002
From the equation:
x' = (g/k)M - x1 ...(2)
g/k = slope
=> g = k(slope) = 8.92 m s^-2
and the uncertainty is +/- 0.73 m s^-2

I also know that S should theoretically be about a third of the mass of the spring (which is 0.0139kg) but i keep getting huge values ranging from 200 to 6000. I don't understand what I'm supposed to do except that it has something to do with the intercept. Any help would be much appreciated! This is just for a practical write up and isn't very important in the experiment but it's the only thing I haven't been able to work out and it's really annoying me...

And let me know if I've left out any information...

 

[Redbelly98]

Welcome to Physics Forums.

In an experiment to determine g using simple harmonic motion using a harmonic oscillator, a motion sensor and data logging equipment. I have all the variables but I can't figure out how to get S in the following equation:
T^2 = ((4pi^2)/k)M + ((4pi^2)/k)S ...(1)

If T² and M are the variables here, then the y-intercept in this equation is _____?

I have a graph of T^2 (the period) vs Mass of the hanging load.
The slope is 1.863 +/- 0.016 s^2 kg^-1
The intercept is 0.006 +/- 0.001
From the above equation: k= 4pi^2/slope
=> k=21.19 +/- 0.18 kg s^-2

I also have a graph of x' (extension of spring) vs. Mass of load.
The slope is 0.421 +/- 0.034 m kg^-1
The intercept is -0.009 +/- 0.002
From the equation:
x' = (g/k)M - x1 ...(2)
g/k = slope
=> g = k(slope) = 8.92 m s^-2
and the uncertainty is +/- 0.73 m s^-2

I also know that S should theoretically be about a third of the mass of the spring (which is 0.0139kg) but i keep getting huge values ranging from 200 to 6000. I don't understand what I'm supposed to do except that it has something to do with the intercept. Any help would be much appreciated! This is just for a practical write up and isn't very important in the experiment but it's the only thing I haven't been able to work out and it's really annoying me...

And let me know if I've left out any information...