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

Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

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 because...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Damped Oscillations01:07

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...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Modes of Standing Waves: II01:04

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.

You might also read

Related Articles

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

Sort by
Same author

Complex bifurcation structures in a Hodgkin-Huxley model of thermally sensitive neurons under periodic perturbation.

Physical review. E·2025
Same author

Temperature effects on neuronal synchronization in seizures.

Chaos (Woodbury, N.Y.)·2024
Same author

Simple and inexpensive microwave setup for industrial based applications: Quantification of flower honey adulteration as a case study.

Scientific reports·2024
Same author

Characterizing the spike timing of a chaotic laser by using ordinal analysis and machine learning.

Chaos (Woodbury, N.Y.)·2024
Same author

Unravelling COVID-19 waves in Rio de Janeiro city: Qualitative insights from nonlinear dynamic analysis.

Infectious Disease Modelling·2024
Same author

Phase synchronization in a sparse network of randomly connected neurons under the effect of Poissonian spike inputs.

Chaos (Woodbury, N.Y.)·2023

Related Experiment Video

Updated: Jun 23, 2026

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

Bouncing ball problem: stability of the periodic modes.

Joaquim J Barroso1, Marcus V Carneiro, Elbert E N Macau

  • 1Associated Plasma Laboratory, National Institute for Space Research, 12227-010, São José dos Campos, SP, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary

The bouncing ball problem reveals complex nonlinear dynamics, including chaotic motion, when a ball collides with a vibrating table. Initial conditions significantly influence whether the ball

More Related Videos

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
08:19

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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

Published on: December 4, 2017

Related Experiment Videos

Last Updated: Jun 23, 2026

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
08:19

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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

Published on: December 4, 2017

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • The bouncing ball problem is a fundamental model in physics.
  • Understanding its dynamics is crucial for various applications.

Purpose of the Study:

  • To provide an overview of the bouncing ball problem.
  • To explore its complex nonlinear behaviors and stability conditions.

Main Methods:

  • Modeling the dynamics using a discrete map of difference equations.
  • Numerical solutions to reveal nonlinear behaviors.
  • Analytical considerations for stability and bifurcation of periodic motions.

Main Results:

  • The system exhibits rich nonlinear behaviors: irregular nonperiodic orbits, subharmonic and chaotic motions, chattering, and unbounded orbits.
  • Periodic motions' stability and bifurcation conditions were determined.
  • Slight changes in initial conditions can lead to transitions from periodic to chaotic orbits.

Conclusions:

  • The bouncing ball problem demonstrates complex dynamics.
  • Nonlinear behaviors are sensitive to initial conditions and system parameters like shaking acceleration and coefficient of restitution.