So, for a school project, I decided to investigate the SHM of a trampoline like system of springs. Basically, I took an ring, affixed eight springs (at equal angle from each other) to a central circular mass, and oscillated the central mass vertically and calculated the spring constant of these vertical oscillations (the effective force constant of the whole system) at different diameters. To my utter shock, I found that the effective force constant seems to vary at a quadratic rate with the radius. Initially, it decreases with diameter, hits a minimum value, then increases with diameter. According to the formula I derived, the variation should be hyperbolic, but my derived formula seems to fail.
Any formulae/help with explaining my experimental trend would be greatly appreciated!