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

Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

363
Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
363
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
Types of Damping01:20

Types of Damping

6.6K
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...
6.6K
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
RLC Series Circuits01:30

RLC Series Circuits

3.1K
An RLC series circuit comprises an inductor, a resistor, and a charged capacitor connected in series. When the circuit is closed, the capacitor begins to discharge through the resistor and inductor by transferring energy from the electric field to the magnetic field. Here, the resistor connected to the circuit causes energy losses; therefore, on the complete discharge of the capacitor, the magnetic field energy acquired by the inductor is less than the original electric field energy of the...
3.1K

You might also read

Related Articles

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

Sort by
Same author

Analytical Solution to a Third-Order Rational Difference Equation.

TheScientificWorldJournal·2023
Same author

Analytical Solution to the Generalized Complex Duffing Equation.

TheScientificWorldJournal·2022
Same author

Perihelion Precessions of Inner Planets in Einstein's Theory and Predicted Values for the Cosmological Constant.

TheScientificWorldJournal·2022
Same author

The Galerkin Method for Solving Strongly Nonlinear Oscillators.

TheScientificWorldJournal·2022
Same author

An Elementary Solution to a Duffing Equation.

TheScientificWorldJournal·2022
Same author

Solution to a Damped Duffing Equation Using He's Frequency Approach.

TheScientificWorldJournal·2022

Related Experiment Video

Updated: Aug 27, 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

Analytical Approximant to a Quadratically Damped Forced Cubic-Quintic Duffing Oscillator.

Alvaro H S Salas1

  • 1Universidad Nacional de Colombia, Fizmako Research Group, Bogota, Colombia.

Thescientificworldjournal
|September 23, 2022
PubMed
Summary

Researchers developed an approximate analytical solution for the cubic-quintic Duffing oscillator. This method accurately estimates solution behavior, including axis crossings, for systems with strong damping and forcing.

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
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

8.6K

Related Experiment Videos

Last Updated: Aug 27, 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
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

8.6K

Area of Science:

  • Nonlinear Dynamics
  • Mechanical Vibrations
  • Applied Mathematics

Background:

  • The cubic-quintic Duffing oscillator is a fundamental model in nonlinear dynamics.
  • Understanding its behavior under strong damping and forcing is crucial for many physical systems.
  • Existing analytical solutions are often limited in scope or accuracy.

Purpose of the Study:

  • To develop an elementary approximate analytical solution for the cubic-quintic Duffing oscillator.
  • To validate the accuracy of the proposed analytical approximant.
  • To utilize the solution for estimating critical points of the system's response.

Main Methods:

  • Formulation of an approximate analytical solution using exponential and trigonometric functions.
  • Numerical simulation using the Runge-Kutta method for comparison.
  • Analysis of solution behavior, specifically focusing on axis-crossing points.

Main Results:

  • An elementary approximate analytical solution was successfully derived for the cubic-quintic Duffing oscillator.
  • The analytical approximant showed good agreement with the Runge-Kutta numerical solution.
  • The approximant effectively estimates the points where the oscillator's solution crosses the horizontal axis.

Conclusions:

  • The proposed analytical solution offers a valuable and accessible method for studying the cubic-quintic Duffing oscillator.
  • This approach provides reliable estimations for key dynamic behaviors, including equilibrium crossings.
  • The findings contribute to a better understanding of damped and forced nonlinear oscillatory systems.