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Damped Oscillations01:07

Damped Oscillations

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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.
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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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An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
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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.
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Forced Oscillations01:06

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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.
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Heart Failure II: Pathophysiology01:29

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Systolic Heart Failure and Compensatory MechanismsSystolic heart failure (also termed HFrEF, Heart Failure with Reduced Ejection Fraction) is the most prevalent type of heart filure. It results in a decreased volume of blood being pumped from the ventricle. The aortic arch and carotid sinuses have baroreceptors that detect reduced blood pressure, triggering the sympathetic nervous system (SNS) to release epinephrine and norepinephrine. Initially, this response aims to boost heart rate and...
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Related Experiment Video

Updated: Oct 5, 2025

Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism
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Diastolic function: modeling left ventricular untwisting as a damped harmonic oscillator.

Forrest N Gamble1, M Rifqi Aufan2, Oleg F Sharifov1

  • 1Department of Medicine, Division of Cardiovascular Disease, University of Alabama at Birmingham, Birmingham, AL, United States of America.

Physiological Measurement
|January 24, 2022
PubMed
Summary

Resistant hypertension increases overall left ventricular (LV) stiffness due to hypertrophy, not intrinsic tissue changes. This study models LV untwisting to assess myocardial stiffness and damping properties in RHTN patients.

Keywords:
cardiovascular MRIdiastolic functionhypertensionleft ventricletorsion

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Area of Science:

  • Cardiovascular Physiology
  • Biomedical Engineering
  • Medical Imaging

Background:

  • Resistant hypertension (RHTN) is associated with adverse cardiac remodeling.
  • Assessing intrinsic myocardial stiffness and relaxation properties is crucial for understanding hypertensive heart disease.

Purpose of the Study:

  • To develop and apply a cardiovascular magnetic resonance imaging (CMR) method to model left ventricular (LV) untwisting as a damped torsional harmonic oscillator.
  • To estimate intrinsic myocardial stiffness (shear modulus) and frictional damping in patients with RHTN compared to controls.

Main Methods:

  • Developed a novel CMR-based model of LV diastolic untwisting as a damped, unforced harmonic oscillator.
  • Measured angular displacement of the LV during diastole in 100 RHTN patients and 36 controls.
  • Calculated myocardial shear modulus, damping constant, and polar moment.

Main Results:

  • Overall LV torsional stiffness was significantly increased in RHTN patients (p=0.001).
  • Myocardial shear modulus (intrinsic stiffness) was not different between RHTN and control groups (p=0.758).
  • RHTN showed increased overall diastolic frictional damping (p<0.001) and polar moment (p<0.001), suggesting hypertrophy as the cause of increased stiffness.

Conclusions:

  • The developed phenomenological method effectively estimates LV intrinsic stiffness and relaxation properties.
  • Increased LV stiffness in RHTN is primarily attributed to cardiac hypertrophy (increased polar moment) rather than intrinsic myocardial tissue changes.
  • This model provides new insights into the mechanical consequences of RHTN on the heart.