A uniform thin square plate of mass
m and side length
a is suspended from a fixed frictionless spherical pivot attached to one of its corners. The plate hangs in equilibrium under the influence of gravity. It is then given a small perturbation so that it performs small oscillations. The resulting motion can be described as a superposition of two independent simple harmonic modes. What is the ratio of the longest possible period of oscillation to the shortest possible period of oscillation?