Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Forced Oscillations01:06

Forced Oscillations

6.7K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.7K
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

2.4K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
2.4K
Damped Oscillations01:07

Damped Oscillations

5.9K
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...
5.9K
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

1.2K
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...
1.2K
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

5.6K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
5.6K
Second Order systems II01:18

Second Order systems II

155
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.
155

You might also read

Related Articles

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

Sort by
Same author

A predator-prey model with age-structured role reversal.

Journal of mathematical biology·2026
Same author

Learning collective variables that respect permutational symmetry.

The Journal of chemical physics·2025
Same author

Predicting molecule size distribution in hydrocarbon pyrolysis using random graph theory.

The Journal of chemical physics·2023
Same author

Computing committors via Mahalanobis diffusion maps with enhanced sampling data.

The Journal of chemical physics·2022
Same author

COVID-19: data-driven dynamics, statistical and distributed delay models, and observations.

Nonlinear dynamics·2020

Related Experiment Video

Updated: Aug 30, 2025

Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels
08:32

Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels

Published on: January 28, 2022

2.5K

Most probable escape paths in periodically driven nonlinear oscillators.

Lautaro Cilenti1, Maria Cameron2, Balakumar Balachandran1

  • 1Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, USA.

Chaos (Woodbury, N.Y.)
|September 1, 2022
PubMed
Summary

Researchers developed a new method to find escape paths in complex mechanical systems. This helps predict transitions between vibrational modes in systems like turbomachinery, crucial for understanding system stability.

More Related Videos

Fabrication and Testing of Microfluidic Optomechanical Oscillators
09:10

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

12.3K
Generation of Local CA1 γ Oscillations by Tetanic Stimulation
08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

9.2K

Related Experiment Videos

Last Updated: Aug 30, 2025

Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels
08:32

Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels

Published on: January 28, 2022

2.5K
Fabrication and Testing of Microfluidic Optomechanical Oscillators
09:10

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

12.3K
Generation of Local CA1 γ Oscillations by Tetanic Stimulation
08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

9.2K

Area of Science:

  • Mechanical Systems Dynamics
  • Nonlinear Oscillators
  • Vibrational Mode Transitions

Background:

  • Mechanical systems, like turbomachinery, are often modeled as arrays of coupled nonlinear oscillators.
  • These systems can exhibit multiple stable vibrational modes, with transitions influenced by random factors.
  • Understanding these transitions is critical for predicting system behavior and preventing failures.

Purpose of the Study:

  • To develop a methodology for identifying the most probable escape paths between vibrational modes.
  • To estimate transition rates in systems with small noise levels.
  • To apply this methodology to arrays of coupled monostable oscillators with specific nonlinearities and forcing.

Main Methods:

  • The study builds upon the action plot method, integrating large deviation theory, optimal control theory, and Floquet theory.
  • The action plot method is extended to handle non-autonomous, high-dimensional systems.
  • A novel approach is proposed to solve optimization problems with discontinuous objective functions on specific manifolds.

Main Results:

  • The methodology successfully computes and visualizes the most probable escape paths between stable vibrational modes.
  • Quasipotential barriers corresponding to these transitions are calculated for systems up to five oscillators.
  • The dependence of the quasipotential barrier height on system parameters is analyzed.

Conclusions:

  • The developed methodology provides a robust framework for analyzing escape dynamics in complex nonlinear systems.
  • This approach enhances the understanding of vibrational mode transitions and their associated energy barriers.
  • The findings are applicable to the design and stability analysis of mechanical systems like turbomachinery.