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4-050-ResonanceBeats-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: Spring 2020 workshop vibration tuning driver resonance forced vibration undamped beats naturl frequency

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Abstract

Resource Image We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

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Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
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Technology
Approach
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Key Scientific Process Skills
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Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

Consider a spring mass dashpot model with mass m kg, resistance c N/(m/s), and spring constant k N/m with a forcing function f(t) in units N to describe the displacement from static equilibrium, y(t).

We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

Now we were interested in what happened as our driver frequency, omega, got close to our natural frequency, omega0, the natural frequency of our system,  and we saw (and heard!) beats in our solution. Well, what happens as omega gets very close, arbitrarily close, omega0?

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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