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.

Hanging a capacitor plate from a spring: a coupled mechanical–electromagnetic oscillator

“…Evaluating this result at the initial instant when Q = Q 0 gives the left-hand side of equation (3).…”

“…Coupled oscillators are a standard topic in the undergraduate physics curriculum. Mass-spring and pendulum systems are commonly discussed, such as the Wilberforce pendulum [1], a pair of simple pendulums connected by a weak link [2], or a linear chain of alternating masses and springs [3]. Inductively-coupled electromagnetic oscillators also lend themselves to rich theoretical predictions [4] and oscilloscope measurements [5].…”

Theoretical and experimental study of the normal modes in a coupled two-dimensional system

“…6 In general physics courses, the topic of coupled systems has been basically analyzed by means of linear 1D models. 7 It is also possible to find a number of works in the literature on the experimental characterization of coupled 1D systems connected to external drivers, 8 i.e. by using video-analysis techniques, 9 electromechanical systems 10 or sensors.…”

Investigation of Compound Relaxation Processes in Crystal Lattice Dynamics of Si Irradiated by Soft X-rays

“…The importance of excited lattice vibrations can be derived from the fact that Si crystal after irradiation can stay in excited states many hours [2,3]. The initial part of dependence of the point defect-producing process in excited states of lattice generated by X-rays play the role of external periodic force, and when its frequency coincides with the frequency of thermal vibrations of atoms placed at neighboring of excited vacancies [14] ω v = 3k/m −γ 2 , the res-onance occurs. Here, k is oscillators constant, γ = c/2m, where c is the coefficient of velocity-dependent damping force, m is the oscillators mass.…”