According to the lab manual, if the mass hanging on the spring is M and the spring has mass m, then the frequency of oscillation is determined by an effective combined mass M + c m with c = 1/3. The value 1/3 is actually approximate, in the limit that the spring mass is much less than the hanging mass. A more accurate calculation, assuming a cylindrical spring of constant mass density, is given by the graph below. The coefficient is actually always greater than 1/3, and approaches this value when M is much larger than m. When M = 0, the limiting value is c = 4/pi². A derivation requires calculus, and is well beyond the scope of Physics 221, but can be found in this PDF document.

Hanging Mass / Spring Mass