Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Damped Oscillations

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Types of Damping

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.

RLC Circuit as a Damped Oscillator

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

Relation between Mathematical Equations and Block Diagrams

Relation between Mathematical Equations and Block Diagrams

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Universal Precision Limits in General Open Quantum Systems.

Physical review letters·2026

Same author

Macroscopic particle transport in dissipative long-range bosonic systems.

Nature communications·2026

Same author

Thermodynamic entropic uncertainty relation.

Physical review. E·2025

Same author

Fundamental Precision Limits in Finite-Dimensional Quantum Thermal Machines.

Physical review letters·2025

Same author

Quantum-computer-based verification of quantum thermodynamic uncertainty relation.

Physical review. E·2025

Same author

Thermomajorization Mpemba Effect.

Physical review letters·2025

Search research articles

Related Experiment Video

Updated: Jan 5, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Uncertainty relations for underdamped Langevin dynamics.

Tan Van Vu¹, Yoshihiko Hasegawa¹

¹Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

Physical Review. E

|October 24, 2019

Summary

We investigated the thermodynamic uncertainty relation in underdamped Langevin dynamics. Dynamical activity significantly influences precision limits, unlike in overdamped systems.

More Related Videos

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Related Experiment Videos

Last Updated: Jan 5, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Area of Science:

Statistical mechanics
Non-equilibrium thermodynamics
Physical systems dynamics

Background:

The thermodynamic uncertainty relation links precision and dissipation in Markovian systems.
Previous studies focused mainly on overdamped dynamics.
Underdamped systems present unique challenges due to inertia.

Purpose of the Study:

Investigate the thermodynamic uncertainty relation for underdamped Langevin dynamics.
Determine the role of dynamical activity in precision-dissipation trade-offs.
Establish bounds on relative fluctuations in steady states.

Main Methods:

Utilized information inequalities to derive theoretical bounds.
Analyzed underdamped Langevin dynamics.
Employed analytical and numerical verification methods.

Main Results:

Proved that relative fluctuation is constrained by entropy production and dynamical activity.
Demonstrated that dynamical activity is crucial for underdamped systems, unlike overdamped ones.
Illustrated findings with single-well potential and driven Brownian particle models.

Conclusions:

The thermodynamic uncertainty relation is modified by dynamical activity in underdamped systems.
This work extends the understanding of precision-dissipation trade-offs beyond overdamped regimes.
The findings have implications for designing precise nanoscale systems.