# Torsional Pendulum Suspended by Two Stranded Wires

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This Demonstration simulates a variation of the classic torsional pendulum.

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Contributed by: Erik Mahieu (February 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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:

.

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