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Damped Oscillations01:07

Damped Oscillations

6.0K
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...
6.0K
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

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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...
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Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

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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
2.5K
Forced Oscillations01:06

Forced Oscillations

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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.
6.8K
Types of Damping01:20

Types of Damping

6.7K
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...
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Second Order systems II01:18

Second Order systems II

171
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.
171

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Related Experiment Video

Updated: Sep 11, 2025

Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice
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Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice

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Resolving Dual Processes in Complex Oscillatory Yielding.

James J Griebler1, Anita S Dobo1, Elizabeth E Miczuga1

  • 1University of Illinois at Urbana-Champaign, Department of Chemical and Biomolecular Engineering, Urbana, Illinois 61801, USA.

Physical Review Letters
|August 18, 2025
PubMed
Summary

Soft materials exhibit complex yielding through two distinct processes: elastic softening at small deformations and true yielding at larger ones. Recovery rheology experiments helped decouple these phenomena.

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Area of Science:

  • Rheology
  • Soft Matter Physics
  • Materials Science

Background:

  • Soft materials often display complex yielding behaviors under stress.
  • Understanding the distinct mechanisms behind multi-step yielding is crucial for material design.

Purpose of the Study:

  • To investigate and elucidate the mechanisms behind the complex two-step yielding observed in soft materials under oscillatory shearing.
  • To differentiate between elastic softening and yielding phenomena.

Main Methods:

  • Oscillatory shearing experiments were performed on soft materials.
  • Recovery rheology data was collected and analyzed.
  • A rheo-physical model was constructed to interpret the experimental observations.

Main Results:

  • The complex two-step yielding was attributed to two independent phenomena.
  • Elastic softening was identified as the first step at small deformations.
  • True yielding was identified as the second step occurring at larger deformations.

Conclusions:

  • The study successfully decoupled the physics of recoverable and unrecoverable processes in soft materials.
  • Recovery experiments provide critical insights into the distinct mechanisms governing complex yielding behaviors.