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3A70.u3 - Bi-Frequency Pendulum

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3A70.u3 - Bi-Frequency Pendulum

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Title3A70.u3 - Bi-Frequency Pendulum
Objective

Demonstrate Second Harmonic Generation and Parametric Excitations.

StatusAvailable
Assembly Instructions
Setup Time5
Operation Time0
Preview Time10
Operation Instructions

​Disturb the pendulum bob in a single direction from its initial equillibrium position and release it. Watch as the energy transfers from one axis to another and back again over time.

ExportableYes
Demo on DimeNo
PIRA 200No
Export Instructions (if different)
HazardsNone
Analysis/Information

​Second Harmonic generation and Parametric Excitations require phase-matching, central symmetry violation, and other tunings.

Proper choice of relationships betweens stick's length h, string length L, and tilt (theta) allows to tune the frequency ratio 2 to 1 for the two linearized eigenmodes. w1 = (g*cos(theta)/(h+L*cos(theta)))^(1/2), and w2 = (g/L)^(1/2).

The Non-Linear aspects have great teaching significance for difficult subjects in the field of optics being analogous to the electron mapping in a medium with passing electromagnetic waves.

Category3 Oscillations
Subcategory3A - Oscillations
KeywordsSecond Harmonic Generation, Non-Linear, Bi-frequency, pendulum
Construction Information
 
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