Mode detuning in systems of weakly coupled oscillators

A system of weakly magnetically coupled oscillating blades is studied experimentally, computationally, and theoretically. It is found that when the uncoupled natural frequencies of the blades are nearly equal, the normal modes 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 than͒ the relative differences between mode frequencies. But if the uncoupled natural frequencies are made to vary ͑detuned͒ in a smooth way such that the total relative spread in natural frequency exceeds the random variations, normal modes are rather easy to find. And if the detuned uncoupled frequencies of the system are parabolically distributed, the modes are found to be shaped like Hermite functions.