Related papers: Theoretical and experimental study of the normal m…
We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two symmetric matrices. We apply it to some simple illustrative…
Experimental analysis of the motion in a system of two coupled oscillators with arbitrary initial conditions was performed and the normal coordinates were obtained directly. The system consisted of two gliders moving on an air track, joined…
The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but…
We present an experimental setup to demonstrate normal modes and symmetry breaking in a two-dimensional pendulum. In our experiment we have used two modes of a single oscillator to demonstrate normal modes, as opposed to two single…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as model for the low-temperature vibrational properties of glass. Exact…
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
Science students must deal with the errors inherent to all physical measurements and be conscious of the need to expressvthem as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
A two-dimensional generalized oscillator with time-dependent parameters is considered to study the two-mode squeezing phenomena. Specific choices of the parameters are used to determine the dispersion matrix and analytic expressions, in…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray…
We present a theory of vibrational modulation of two-dimensional coherent Fourier transformed electronic spectra. Based on an expansion of the system's energy gap correlation function in terms of Huang-Rhys factors, we explain the…
This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely, the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for…
The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and…
The universal conductance fluctuations of quasi-two-dimensional systems are analyzed with experimental considerations in mind. The traditional statistical metrics of these fluctuations (such as variance) are shown to have large statistical…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…