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

Introduction to Differential Equations01:20

Introduction to Differential Equations

541
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
541
Second Order systems II01:18

Second Order systems II

542
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.
542
Forced Oscillations01:06

Forced Oscillations

6.3K
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.
6.3K
Second Order systems I01:20

Second Order systems I

800
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
800
Second-Order Circuits01:17

Second-Order Circuits

4.4K
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
4.4K
Damped Oscillations01:07

Damped Oscillations

6.2K
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...
6.2K

You might also read

Related Articles

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

Sort by
Same author

Exploratory topological data analysis for spatio-temporal knowledge discovery in epidemiology.

Spatial and spatio-temporal epidemiology·2026
Same author

Comparative stability analysis of mixed clustering algorithms for Malaysian dengue epidemiology using topological descriptors.

Acta tropica·2025
Same author

Comparative analysis of Ball Mapper and conventional Mapper in investigating air pollutants' behavior.

Environmental monitoring and assessment·2025
Same author

Persistent Homology-Based Machine Learning Method for Filtering and Classifying Mammographic Microcalcification Images in Early Cancer Detection.

Cancers·2023
Same author

Hybridization of hierarchical clustering with persistent homology in assessing haze episodes between air quality monitoring stations.

Journal of environmental management·2022
Same author

Using persistent homology as preprocessing of early warning signals for critical transition in flood.

Scientific reports·2021

Related Experiment Video

Updated: Apr 26, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

10.3K

Oscillation theorems for second order nonlinear forced differential equations.

Ambarka A Salhin1, Ummul Khair Salma Din1, Rokiah Rozita Ahmad1

  • 1School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.

Springerplus
|August 1, 2014
PubMed
Summary

This study introduces new oscillation theorems for second-order forced nonlinear differential equations. The findings expand upon and enhance existing literature in the field.

Keywords:
Forced nonlinear differential equations of second orderOscillation

More Related Videos

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

12.6K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.1K

Related Experiment Videos

Last Updated: Apr 26, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

10.3K
Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

12.6K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.1K

Area of Science:

  • Mathematics
  • Differential Equations

Background:

  • Oscillation theory is crucial for understanding the behavior of solutions to differential equations.
  • Existing literature provides foundational results for second-order forced nonlinear differential equations.

Purpose of the Study:

  • To investigate a specific class of second-order forced nonlinear differential equations.
  • To develop novel oscillation theorems for these equations.

Main Methods:

  • Analysis of second-order forced nonlinear differential equations.
  • Development of new mathematical criteria for oscillation.

Main Results:

  • Several new oscillation theorems were established.
  • The obtained theorems are applicable to a defined class of equations.

Conclusions:

  • The new oscillation theorems generalize and improve upon existing results.
  • This work contributes to the advancement of oscillation theory for nonlinear differential equations.