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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.
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Physical Pendulum

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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°.
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Related Experiment Video

Updated: Oct 5, 2025

Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light

Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light

Published on: September 20, 2017

A Self-Stabilized Inverted Pendulum Made of Optically Responsive Liquid Crystal Elastomers.

Quanbao Cheng¹, Lin Zhou², Kai Li¹

¹Department of Civil Engineering, Anhui Jianzhu University, Hefei, China.

Frontiers in Robotics and AI

|January 28, 2022

Summary

This study introduces a self-stabilized inverted pendulum using an optically responsive liquid crystal elastomer bar. This novel system achieves stability through self-sustained oscillation, eliminating the need for complex controllers.

Keywords:

inverted pendulum liquid crystal elastomer optically-responsive self-sustained motion stabilization

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Last Updated: Oct 5, 2025

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Area of Science:

Materials Science
Mechanical Engineering
Nonlinear Dynamics

Background:

Inverted pendulum stabilization is crucial for engineering applications but inherently challenging due to instability.
Traditional methods like Kapitza's pendulum often require complex control systems.

Purpose of the Study:

To investigate the self-stabilization of an inverted pendulum using a liquid crystal elastomer (LCE) bar.
To explore the mechanism and critical conditions for self-sustained oscillation in this system.

Main Methods:

Formulation of a theoretical model for the LCE inverted pendulum based on established dynamic LCE models.
Numerical calculations to analyze system behavior and stability.

Main Results:

The LCE inverted pendulum system transitions to either an unstable static state or a self-stabilized oscillation state.
Self-stabilized oscillation arises from the reversal of the gravity moment due to the pendulum's movement.
Critical conditions for triggering self-stabilized oscillation and parameter effects on stability were investigated.

Conclusions:

The self-stabilized LCE inverted pendulum offers a controller-free solution for stabilization.
This system has potential applications in robotics, aerospace, and military industries.