I extend a warm greeting to all of you. I just carried out a simple harmonic motion experience at lab. We're told to find out the relationship between Period and Mass. That thing is I've always found the period formula as:
$$ T=2π\sqrt{\frac{m }{k} } $$
However, I found this formula at my lab's guide.
$$ T= 2π\sqrt{\frac{m + \frac{M}{3}}{k} } $$
Were $ M $ is the mas of the spring. I have not idea where this can come from. I only want to know some hints in case you know something about it.
I appreciate you helping me out.