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Forced Oscillations

Forced Oscillations

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.

Damped Oscillations

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...

Oscillations In An LC Circuit

Oscillations In An LC Circuit

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

Oscillations about an Equilibrium Position

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...

Simple Harmonic Motion

Simple Harmonic Motion

Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator is given...

Design Example: Underdamped Parallel RLC Circuit

Design Example: Underdamped Parallel RLC Circuit

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...

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Related Experiment Video

Updated: May 22, 2026

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

Frequency stabilization in nonlinear micromechanical oscillators.

Dario Antonio¹, Damián H Zanette, Daniel López

¹Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA.

Nature Communications

|May 3, 2012

Summary

By coupling vibrational modes, researchers stabilized nonlinear micromechanical resonators. This innovation enhances frequency stability in micro-oscillators, crucial for advanced electronics.

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Fabrication and Testing of Microfluidic Optomechanical Oscillators

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Area of Science:

Physics
Electrical Engineering
Materials Science

Background:

Mechanical oscillators are vital components in electronic devices, providing stable frequency outputs.
Quartz crystals have traditionally dominated, but micromechanical resonators offer miniaturization and integration benefits.
Microscale resonators often suffer from nonlinearities degrading frequency stability.

Purpose of the Study:

To investigate a method for stabilizing the frequency of nonlinear self-sustaining micromechanical resonators.
To leverage internal resonance for improved oscillator performance.

Main Methods:

Coupling two distinct vibrational modes within micromechanical resonators.
Utilizing internal resonance phenomena to mitigate nonlinear effects.

Main Results:

Demonstrated successful stabilization of oscillation frequency in nonlinear micromechanical resonators.
Showcased a new strategy for engineering low-frequency noise oscillators.

Conclusions:

Internal resonance coupling effectively stabilizes nonlinear micromechanical resonators.
This approach capitalizes on intrinsic nonlinearities for enhanced oscillator performance.