Abstract

We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 3-026-SpringInverseProblem-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/3XFZ-RZ66

  BibTex | EndNote

Article Context

Resource Type

• Modeling Scenario

Differential Equation Type

• ODE
• Second
• Linear
• Constant Coeff
• Homogeneous

Technique

• Eigen Methods

Qualitative Analysis

• Other

Application Area

• Engineering
• Modeling (general)
• Physics

Course

• Differential Equations
• Modeling

Course Level

• Introductory
• Upper Level
• High School

Lesson Length

• One class period

Technology

• Mathematica

Approach

• Guided

Skills

• Data analysis
• Other

Key Scientific Process Skills

• Asking a question
• Formulating hypotheses

Assessment Type

• Homework
• Written assignment: Report

Pedagogical Approaches

• Guided inquiry/investigation

Vision and Change Core Competencies - Ability

• Create and develop models
• Use quantitative reasoning

Principles of How People Learn

• Motivates student to learn material
• Focuses student on the material to be learned

Bloom's Cognitive Level

• Application & Analysis

Description

This is an example of an inverse problem in which we are given data and we seek to estimate a parameter in the model so as to fit this data with a model and thus validate the model.

Article Files

• 3-026-S-SpringInverseProblem-StudentVersion.pdf(PDF | 390 KB)
• 3-026-S-SpringInverseProblem-StudentVersion.tex(TEX | 6 KB)
• 3-026-T-Mma-SpringInverseProblem-TeacherVersion.nb (Instructors only)(NB | 236 KB)
• 3-026-T-Mma-SpringInverseProblem-TeacherVersion.pdf (Instructors only)(PDF | 209 KB)
• 3-026-T-SpringInverseProblem-TeacherVersion.pdf (Instructors only)(PDF | 397 KB)
• 3-026-T-SpringInverseProblem-TeacherVersion.tex (Instructors only)(TEX | 6 KB)
• simiode.cls(CLS | 7 KB)
• SimiodeLogo.jpg(JPG | 271 KB)
• SpringMysteryPic.jpg(JPG | 9 KB)
• License terms

Authors

Author(s): Brian Winkel

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

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