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3-105-FrequencyResponse-ModelingScenario

Author(s): Brian Winkel

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

Keywords: transient dynamics circuit spring mass driver frequency response amplitude steady state

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Abstract

Resource Image We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

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Article Context

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

Description

Engineers are often interested in the response of a system to inputs. Consider an RLC circuit in which a voltage input drivers the circuit at a certain frequency.

What is the gain or system response to a particular driver's frequency?

Or consider a mathematical model consisting of a second order differential equation for a spring-mass model for a building structure which is driven by an input force with low frequency, think earthquake at 10 Hz.

What is the amplitude of the structures response?

A ride over a rough rippled dirt road drives the shock absorber of the vehicle differently at different frequencies of bumps in the road? Can this hurt the vehicle or make the ride very uncomfortable?

We offer the steps to compute the frequency response or maximum steady state amplitude in a spring mass dashpot system as an imagery example.

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Authors

Author(s): Brian Winkel

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

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