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Related Concept Videos

Torsional Pendulum01:09

Torsional Pendulum

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
Damped Oscillations01:07

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...
Bending and Torsional Moments01:20

Bending and Torsional Moments

Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions.
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...
Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
Next,...
Simple Harmonic Motion01:21

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...
Physical Pendulum01:06

Physical Pendulum

When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
When dealing with complicated systems, the mass moment of inertia is an important parameter, as it describes the mass...

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Related Experiment Video

Updated: May 16, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

A physics-based link model for tree vibrations.

Kevin D Murphy1, Mark Rudnicki

  • 1Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139, USA. kdm@engr.uconn.edu

American Journal of Botany
|December 1, 2012
PubMed
Summary
This summary is machine-generated.

A new mathematical model for tree vibrations offers insights into stability and experimental data interpretation. This physics-based approach uses Newtonian analysis and modal analysis for accurate vibration response prediction.

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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

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Last Updated: May 16, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
09:32

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

Area of Science:

  • Biomechanics
  • Structural Dynamics
  • Arboreal Physics

Background:

  • Understanding tree vibrations is crucial for assessing structural integrity and interpreting experimental data.
  • Existing models may not fully capture the complex dynamics of tree structures, including trunk and branch interactions.

Purpose of the Study:

  • To introduce a novel mathematical model for analyzing tree vibrations.
  • To enhance the understanding of the response structure in tree dynamics.
  • To provide a tool for stability assessment and experimental data interpretation in arboreal science.

Main Methods:

  • Developed a physics-based model using Newtonian analysis for trunk and N-branch motion.
  • Derived (N+1) nonlinear, coupled differential equations to describe tree response.
  • Employed linearization, modal analysis for analytical solutions, and numerical methods for validation and large amplitude vibrations.

Main Results:

  • Presented a new physics-based mathematical model for tree vibrations.
  • Demonstrated that tree response for small motions can be synthesized from mode shapes and frequencies.
  • Highlighted limitations of linear theory and presented numerical solutions for large amplitude vibrations.

Conclusions:

  • The model effectively incorporates critical physics into tree vibration analysis.
  • The study elucidates the modal nature of vibration response in trees.
  • Limitations of linear solutions were identified and discussed, paving the way for more comprehensive analyses.