相关论文: The motion of two masses coupled to a massive spri…
We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction…
The non-evanescent vibration, evanescent vibration and forced vibration of an oscillator attached to the massless spring are always discussed in general mechanics courses. In this article, we focus on the heavy-spring conditions. We first…
We examine the problem of motion of an oscillating mass object provided no external force is applied to it. Calculations directly lead to the conclusion that the body accelerates in each system of reference except for the rest reference…
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear…
We introduce a novel, two-mass system that slides up an inclined plane while its center of mass moves down. The system consists of two identical masses connected by an ideal string symmetrically placed over a corner-shaped support. This…
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…
We analyze a simple problem in elasticity: the \emph{initial} motion of an elastic bar that after being hanged from an end is suddenly released. In a second problem a point mass is attached on the top of the bar. The analytical solutions…
We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604].…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
The problem of finding the frequencies of small longitudinal oscillations of a spring having a finite mass and stiffness, attached at one end to a wall and at the other end to a body of finite mass, is discussed. This problem was repeatedly…
The spring-mass system studied in undergraduate physics laboratories may show complex dynamics due to the simultaneous action of gravitational, elastic, and torsional forces, in addition to air friction. In this paper, we describe a…
Within the context of linear elasticity we show that a two-terminal network of springs and masses, can respond exactly the same as a normal spring, but with a frequency dependent spring constant. As a consequence a network of such springs…
The spring-mass system studied in undergraduate physics laboratories may exhibit complex dynamics due to the simultaneous action of gravitational and elastic forces in addition to air friction. In the first part of this paper, we describe a…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
The harmonic oscillator plays a central role in physics describing the dynamics of a wide range of systems close to stable equilibrium points. The nonrelativistic one-dimensional spring-mass system is considered a prototype representative…
In the present article we determine the exact shape of an ideal spring suspended at both ends. Historically, this goes under the name of Elastica problem. The total energy of the suspended spring is a functional depending on two independent…
We introduce a simple model of self-propelled agents connected by linear springs, with no explicit alignment rules. Below a critical noise level, the agents self-organize into a collectively translating or rotating group. We derive…
A general expression for the elastic potential energy of a helical spring is derived using the basic concepts of elasticity theory and geometry. Both the translational and the rotational displacement of the spring's moving ends are…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
We study the motion of the system, S, constituted by a rigid body, B, containing in its interior a viscous compressible fluid, and moving in absence of external forces. Our main objective is to characterize the long time behavior of the…