Direct observation of normal modes in coupled oscillators

Abstract

We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus. The method consists of applying a frequency dependent force to the system and using the resonance to excite each mode separately. The frequency of the excited mode is determined by measuring the resonance frequency of the system. We found that the measured normal mode frequencies of coupled oscillators exhibiting two and three normal modes are in very good agreement with the theoretical estimates. The method is suitable for undergraduate students with an elementary knowledge of differential equations.