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Concept# Restoring force

Résumé

In physics, the restoring force is a force that acts to bring a body to its equilibrium position. The restoring force is a function only of position of the mass or particle, and it is always directed back toward the equilibrium position of the system. The restoring force is often referred to in simple harmonic motion. The force responsible for restoring original size and shape is called the restoring force.
An example is the action of a spring. An idealized spring exerts a force proportional to the amount of deformation of the spring from its equilibrium length, exerted in a direction oppose the deformation. Pulling the spring to a greater length causes it to exert a force that brings the spring back toward its equilibrium length. The amount of force can be determined by multiplying the spring constant, characteristic of the spring, by the amount of stretch, also known as Hooke's Law.
Another example is of a pendulum. When a pendulum is not swinging all the forces acting on it are

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Cours associés (13)

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Séances de cours associées (26)

László Forró, Sylvia Jeney, Andrzej Kulik, Branimir Lukic

Thermal position fluctuations of a colloidal particle in an optical trap are measured with microsecond resolution using back-focal-plane interferometry. The mean-square displacement MSD(t) and power spectral density are in excellent agreement with the theory for a Brownian particle in a harmonic potential that accounts for hydrodynamic memory effects. The motion of a particle is dominated at short times by memory effects and at longer times by the potential. We identify the time below which the particle's motion is not influenced by the potential, and find it to be approximately tau_k/20, where tau_k is the relaxation time of the restoring force of the potential. This allows us to exclude the existence of free diffusive motion (MSD(t) proprtional t) even for a sphere with a radius as small as 0.27 µm in a potential as weak as 1.5 µN/m. As the physics of Brownian motion can be used to calibrate an optical trap, we show that neglecting memory effects leads to an underestimation of more than 10% in the detector sensitivity and the trap stiffness for an experiment with a micrometer-sized particle and a sampling frequency above 200 kHz. Furthermore, these calibration errors increase in a nontrivial fashion with particle size, trap stiffness, and sampling frequency. Finally, we present a method to evaluate calibration errors caused by memory effects for typical optical trapping experiments.

2007, , , , ,

We define isotropic springs to be central springs having the same restoring force in all directions. In previous work, we showed that isotropic springs can be advantageously applied to horological time bases since they can be used to eliminate the escapement mechanism [7]. This paper presents our designs based on planar serial 2-DOF linear isotropic springs. We propose two architectures, both based on parallel leaf springs, then evaluate their isotropy defect using firstly an analytic model, secondly finite element analysis and thirdly experimental data measured from physical prototypes. Using these results, we analyze the isotropy defect in terms of displacement, radial distance, angular separation, stiffness and linearity. Based on this analysis, we propose improved architectures stacking in parallel or in series duplicate copies of the original mechanisms rotated at specific angles to cancel isotropy defect. We show that using the mechanisms in pairs reduces isotropy defect by one to two orders of magnitude. (C) 2015 The Authors. Published by Elsevier Inc.

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Mohamed Gamal Abdelrahman Ahmed Zanaty

Mechanical oscillator (1) for a timepiece comprising an inertial mass (3) arranged to oscillate about a neutral position under the effect of a restoring force provided by at least one elastic element (5),characterised in that said mechanical oscillator (1) further comprises a compensation spring (11) pivotably linked to said inertial mass (3) by means of a substantially rigid first connecting bar (15), said compensation spring (11) and said first connecting bar (15) being arranged so as to apply a compensating force to said inertial mass (3) which varies in function of displacement of said inertial mass (3) from its neutral position.This arrangement permits tuning of the isochronism and thus reduction and/or elimination of the isochronism defect of the oscillator typically caused by nonliearity of the restoring force provided by the elastic element (55)

2020