Torsional Pendulum Suspended by Two Stranded Wires

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration simulates a variation of the classic torsional pendulum.


A disk hangs on a strand of two wires. The disk is given an initial angular displacement and released from rest, resulting in a harmonic motion similar to that of a torsional pendulum.

The potential energy of this system changes cyclically due to the variation in length of the strand, from the twisting and untwisting of the wires.

The changes in potential energy are compensated by changes in the kinetic energy of the rotating disk, with the total energy of the system remaining constant.

Friction between the wires and air drag are not considered.


Contributed by: Erik Mahieu (February 2017)
Open content licensed under CC BY-NC-SA



This system has one degree of freedom, , the angular displacement of the suspended disk at time .

The potential energy of the system is .

is the effective length of the strand after twisting by the angle : , where

is the length of the untwisted strand, and

is the radius of the strand or the distance between the wires.

The kinetic energy of the system is , where

is the mass of the disk,

is the radius of the disk,

is the width of the disk, and

is its density.

The Lagrangian of this system is .

Substituting this in the Euler–Lagrange equations for gives:



This results in the equation of motion:


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.