How Is the Constant 'c' Derived in Spring Oscillation Calculations?

[ramarlon89]

We have been given a table listing the extension and 3 times for 20 oscillations without the mass on the spring stated. I have used this to find an average time then /20 to find t for 1 oscillation, then plotted a t²/x(extension) graph. I have inserted a trend line to find y=mx+c = y=3.8001x + 0.0292. We have been told that c = 4pi²m_spring/k (k=25 N m^-1) rearrange so m_spring = ck/4pi² = 0.01849111601kg

My questions is where does the c = 4pi²m_spring/k come from, I can't find any reference to it at all, I know my answer is right but I would like an understanding of it instead of just writing c = 4pi²m_spring/k as if it's fact. Thanks

 

[haruspex]

Check this out: http://en.m.wikipedia.org/wiki/Effective_mass_(spring–mass_system)