An experiment is described which studies the dynamical behavior of a soft spring. This experiment has proved valuable as a project in a junior or senior physics laboratory. The results demonstrate the inadequacy of both the elementary formula for the period and the modified formula containing a correction term for the mass of the spring. A simple theoretical model is presented which yields results in agreement with experiment. The analysis uses mathematics that the students have been learning in parallel courses. The simplicity of the experiment serves to highlight the interplay of physics and mathematics. Most physics departments already have the elementary equipment needed.