15.3 Angular Simple Harmonic Oscillator

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Last updated 6:26 PM on 6/3/26
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4 Terms

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Angular Harmonic Oscillator

A type of harmonic oscillator in which a disk oscillates about an equilibrium point with respect to a change in theta (as opposed to a linear distance like spring-mass linear oscillator would across a distance delta(X)).



<p>A type of harmonic oscillator in which a disk oscillates about an equilibrium point with respect to a change in theta (as opposed to a linear distance like spring-mass linear oscillator would across a distance delta(X)). </p><p></p><p></p>
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Torsion Pendulum

A torsion pendulum is a type of oscillator in which the twisting of the string (the torsion force) generates oscillatory behavior; in this instance, the restoring force is not given by a spring (like with a mass-spring system), but rather with a restoring torque.



<p>A torsion pendulum is a type of oscillator in which the twisting of the string (the torsion force) generates oscillatory behavior; in this instance, the restoring force is not given by a spring (like with a mass-spring system), but rather with a restoring torque. </p><p></p><p></p>
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Restoring Torque and the Torsion Constant

The torsion constant (Kappa) is dependent on the length, diameter, and the material of the suspension wire itself.


The restoring torque (tau) is the product of the torsion constant and the displacement angle


This relationship is the angular analogue to the linear spring-force relationship:


Torque is the restoring force in an angular context; fS is the restoring force in a linear context


Kappa is the angular constant; k is the linear constant


Theta is the angular displacement; x is the linear displacement


<p>The torsion constant (Kappa) is dependent on the length, diameter, and the material of the suspension wire itself. </p><p></p><p>The restoring torque (tau) is the product of the torsion constant and the displacement angle</p><p></p><p>This relationship is the angular analogue to the linear spring-force relationship:</p><p></p><p>Torque is the restoring force in an angular context; f<sub>S</sub> is the restoring force in a linear context </p><p></p><p>Kappa is the angular constant; k is the linear constant</p><p></p><p>Theta is the angular displacement; x is the linear displacement </p><p></p>
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Period of a Torsion Pendulum


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