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Physical Pendulum

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...

Simple Pendulum

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 Pendulum

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...

Knee Joint

Knee Joint

The knee joint is the most complicated joint in the body. It consists of three articulations– two tibiofemoral and one patellofemoral. As is characteristic of synovial joints, the knee joint has a thin articular capsule that partially surrounds this joint cavity. Additionally, several ligaments, muscles, and cartilaginous structures support the movement of the knee.
A total of seven ligaments support the knee joint. The patellar ligament, which is also attached to the quadriceps femoris...

Predicting Molecular Geometry

Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

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Related Experiment Video

Updated: Feb 7, 2026

In vivo Measurement of Knee Extensor Muscle Function in Mice

In vivo Measurement of Knee Extensor Muscle Function in Mice

Published on: March 4, 2021

Predictive value of the pendulum test for assessing knee extensor spasticity.

Alyssa Whelan¹, Andrew Sexton², Melony Jones³

¹Faculty of Kinesiology, University of New Brunswick, Fredericton, NB, Canada.

Journal of Neuroengineering and Rehabilitation

|July 20, 2018

Summary

The pendulum test effectively detects knee extensor spasticity in neurological patients, irrespective of flexor spasticity. However, its accuracy in grading spasticity levels may be limited.

Keywords:

Classification Knee extensor Knee flexor Logistic regression Modified Ashworth scale Pendulum test Receiver operator characteristic Relaxation index Spasticity

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In vivo Measurement of Knee Extensor Muscle Function in Mice

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Breathing-controlled Electrical Stimulation BreEStim for Management of Neuropathic Pain and Spasticity

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Published on: January 10, 2013

Area of Science:

Neurology
Rehabilitation Medicine
Biomechanics

Background:

The pendulum test is a common method for assessing knee extensor spasticity.
Its effectiveness in detecting spasticity in neurologically impaired patients and the influence of co-existing flexor spasticity remain unclear.

Purpose of the Study:

To evaluate the extent to which pendulum test metrics can detect knee extensor spasticity.
To determine if flexor spasticity affects pendulum test outcomes in patients with neurological conditions.

Main Methods:

Retrospective analysis of 131 knees from 93 patients with neurological conditions.
Collected Modified Ashworth Scale (MAS) scores for extensors/flexors and pendulum test metrics (relaxation index, 1st flexion amplitude, plateau angle).
Statistical analyses included ANOVA and ANCOVA to assess influences of flexor spasticity, age, injury duration, strength, and range of motion; ROC and logistic regression were used for classification.

Main Results:

Pendulum test metrics for knee extensors were not significantly influenced by flexor spasticity, age, injury duration, strength, or range of motion.
Metrics like relaxation index (RI), 1st flexion amplitude (F1amp), and plateau angle (Plat) showed over 70% accuracy in detecting the presence of spasticity.
Classification accuracy for grading spasticity severity was less than 70%, with F1amp and Plat performing better independently than RI alone.

Conclusions:

The pendulum test demonstrates good predictive value for identifying the presence of extensor spasticity, independent of flexor spasticity.
The utility of the pendulum test for grading spasticity severity using current metrics may be limited.
Further research is needed to ascertain the pendulum test's suitability for quantifying more severe spasticity.