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

Second-Order Circuits01:17

Second-Order Circuits

1.4K
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...
1.4K
Second Order systems II01:18

Second Order systems II

115
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.
115
Second-order Op Amp Circuits01:19

Second-order Op Amp Circuits

358
Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.
The analysis of such circuits follows a systematic approach, similar to the second-order RLC circuits. In practical scenarios, bulky inductors are rarely employed due to their size and weight. This means...
358
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

1.0K
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...
1.0K
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

306
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...
306
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

900
A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
900

You might also read

Related Articles

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

Sort by
Same author

Long-acting lenacapavir protects macaques against intravenous challenge with simian-tropic HIV.

EBioMedicine·2023
Same author

Nomogram of uveal melanoma as prediction model of metastasis risk.

Heliyon·2023
Same author

Dual-Responsive Drug-Delivery System Based on PEG-Functionalized Pillararenes Containing Disulfide and Amido Bonds for Cancer Theranostics.

Chembiochem : a European journal of chemical biology·2023
Same author

Discovery of MK-8768, a Potent and Selective mGluR2 Negative Allosteric Modulator.

ACS medicinal chemistry letters·2023
Same author

Common and distinct functional brain network abnormalities in adolescent, early-middle adult, and late adult major depressive disorders.

Psychological medicine·2023
Same author

Integrating Pillar[5]arene and BODIPY for a Supramolecular Nanoplatform To Achieve Synergistic Photodynamic Therapy and Chemotherapy.

Chembiochem : a European journal of chemical biology·2023

Related Experiment Video

Updated: Jul 12, 2025

Fabrication and Testing of Microfluidic Optomechanical Oscillators
09:10

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

12.2K

On-chip all-optical second-order ordinary differential equation solver based on a single microdisk resonator.

Jiahao Zhou, Pengxing Guo, Jingsi Li

    Optics Express
    |October 20, 2023
    PubMed
    Summary

    This study introduces a compact all-optical solver for second-order ordinary differential equations (SODEs) using a single microdisk resonator. The device efficiently solves both constant and complex coefficient SODEs, offering tunable solutions with minimal power.

    More Related Videos

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
    07:42

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

    Published on: December 15, 2021

    3.1K
    Label-free Single Molecule Detection Using Microtoroid Optical Resonators
    08:53

    Label-free Single Molecule Detection Using Microtoroid Optical Resonators

    Published on: December 29, 2015

    9.3K

    Related Experiment Videos

    Last Updated: Jul 12, 2025

    Fabrication and Testing of Microfluidic Optomechanical Oscillators
    09:10

    Fabrication and Testing of Microfluidic Optomechanical Oscillators

    Published on: May 29, 2014

    12.2K
    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
    07:42

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

    Published on: December 15, 2021

    3.1K
    Label-free Single Molecule Detection Using Microtoroid Optical Resonators
    08:53

    Label-free Single Molecule Detection Using Microtoroid Optical Resonators

    Published on: December 29, 2015

    9.3K

    Area of Science:

    • Photonics
    • Optical Computing
    • Nonlinear Optics

    Background:

    • Solving complex differential equations is crucial in science and engineering.
    • Traditional methods often require bulky or power-intensive setups.
    • All-optical approaches offer potential for high-speed computation.

    Purpose of the Study:

    • To propose and validate an all-optical solver for second-order ordinary differential equations (SODEs).
    • To demonstrate the device's capability for solving both constant and complex coefficient SODEs.
    • To highlight the compact size and tunable nature of the proposed solver.

    Main Methods:

    • Utilizing a single microdisk resonator for all-optical SODE solving.
    • Employing Gaussian and super-Gaussian optical pulses as input signals.
    • Analyzing solutions for constant and complex coefficient SODEs.
    • Investigating the influence of pulse width and demonstrating tunable solutions via power control.

    Main Results:

    • The proposed microdisk resonator structure effectively solves constant and complex coefficient SODEs.
    • Solutions obtained optically show good agreement with mathematical calculations.
    • Tunable solutions for complex-coefficient SODEs are achieved with <10 mW tuning power.
    • The device footprint is significantly smaller (20x30 μm²) than existing units, with a Q-factor up to 9.8x10⁴.

    Conclusions:

    • The single microdisk resonator offers a compact and efficient solution for SODE solving.
    • This approach simplifies fabrication by avoiding resonator cascading and alignment issues.
    • The device provides a versatile platform for solving a wider range of SODE problems, including those with complete derivative terms.