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Related Concept Videos

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...
Simple Pendulum01:10

Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line.
The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum is...
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...
Equilibrium and Balance01:15

Equilibrium and Balance

The inner ear assumes dual functionalities of auditory perception and equilibrium maintenance. The vestibule is the organ responsible for balance. This organ contains mechanoreceptors, specifically hair cells, endowed with stereocilia, which aid in deciphering information regarding the position and motion of our heads. Two intrinsic components, the utricle and saccule, help perceive head position, while the semicircular canals track head movement. Neurological messages initiated in the...
Real-World Applications of Power Series01:27

Real-World Applications of Power Series

The motion of a simple pendulum is governed by Newton’s Second Law in its rotational form, which relates the net torque on the bob to its angular acceleration. This physical law gives rise to a second-order differential equation in which the angular acceleration is proportional to the sine of the displacement angle.Because of the sin(𝜃) term, the governing equation is a nonlinear differential equation, which is difficult to solve analytically. To simplify the mathematical model, the sine...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

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Related Experiment Video

Updated: Jun 22, 2026

Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

The time-delayed inverted pendulum: implications for human balance control.

John Milton1, Juan Luis Cabrera, Toru Ohira

  • 1Joint Science Department, W. M. Keck Science Center, The Claremont Colleges, Claremont, California 91711, USA.

Chaos (Woodbury, N.Y.)
|July 2, 2009
PubMed
Summary
This summary is machine-generated.

Human balance control, even in simple models like the inverted pendulum, is unstable due to time delays. This suggests complex, adaptive neural control mechanisms are essential for maintaining upright posture.

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Last Updated: Jun 22, 2026

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Area of Science:

  • Biomechanics
  • Neuroscience
  • Control Theory

Background:

  • The inverted pendulum model is a fundamental tool for understanding human balance.
  • Maintaining upright posture involves complex control systems that counteract instability.

Purpose of the Study:

  • To investigate the role of time-delayed feedback in balance control across different experimental paradigms.
  • To explore the underlying mechanisms of instability in human postural control.

Main Methods:

  • Analysis of mechanical inverted pendulums with time-delayed control.
  • Examination of stick balancing at the fingertip.
  • Measurement of human postural sway during quiet standing using the center of pressure (COP).
  • Calculation of transfer functions and Hurst exponents to quantify movement dynamics.

Main Results:

  • All three paradigms demonstrated that the upright fixed point is unstable.
  • Instability was observed even when mathematical models predicted stability.
  • Human stick balancing met the condition for instability (time delay > critical delay), but other paradigms did not.

Conclusions:

  • The balanced state is a complex, time-dependent state, not a simple fixed-point attractor.
  • A common cause of instability is the difficulty of simultaneously controlling pendulum angle and controller position with time-delayed feedback.
  • Neural control likely involves adaptive mechanisms with thresholds for corrective actions, influenced by noise and time delays.