Mode detuning in systems of weakly coupled oscillators

A system of weakly magnetically coupled oscillating blades is studied exper imentally, computationally, and theoretically. It is found that when the un coupled natural frequencies of the blades are nearly equal, the normal mode s produced by the coupling are almost impossible to find experimentally if the random variation level in the system parameters is on the order of (or larger than) the relative differences between mode frequencies. But if the uncoupled natural frequencies are made to vary (detuned) in a smooth way su ch that the total relative spread in natural frequency exceeds the random v ariations, normal modes are rather easy to find. And if the detuned uncoupl ed frequencies of the system are parabolically distributed, the modes are f ound to be shaped like Hermite functions. (C) 2001 American Association of Physics Teachers.