Abstract

We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and cost.

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 3-031-SpringCost-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/N71R-J453

  BibTex | EndNote

Article Context

Resource Type

• Modeling Scenario

Differential Equation Type

• ODE
• Second
• Linear
• System
• Nonhomogeneous

Technique

• Eigen Methods
• Initial Value Problems
• Parameter Estimation

Qualitative Analysis

• Equilibrium
• Stability
• Graphical analysis
• Parameters

Application Area

• Engineering

Course

• Differential Equations
• Modeling

Course Level

• Introductory
• Upper Level
• High School

Lesson Length

• One class period

Technology

• Mathematica

Approach

• Guided

Skills

• Data analysis

Key Scientific Process Skills

• Asking a question
• Formulating hypotheses
• Predicting outcomes
• Gathering data/making observations

Assessment Type

• Homework
• Written assignment: Report

Pedagogical Approaches

• Guided inquiry/investigation

Vision and Change Core Competencies - Ability

• Create and develop models
• Use quantitative reasoning
• Design simulations

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

We seek to identify and satisfy a number of technical issues w.r.t. a spring mass dashpot model for a car suspension or shock absorber system. For example damping and overdamping, as well as spring performance.

Article Files

• 3-031-S-SpringCost-StudentVersion.pdf(PDF | 391 KB)
• 3-031-S-SpringCost-StudentVersion.tex(TEX | 7 KB)
• 3-031-T-Mma-SpringCost-TeacherVersion.nb (Instructors only)(NB | 2 MB)
• 3-031-T-Mma-SpringCost-TeacherVersion.pdf (Instructors only)(PDF | 961 KB)
• 3-031-T-SpringCost-TeacherVersion.pdf (Instructors only)(PDF | 393 KB)
• 3-031-T-SpringCost-TeacherVersion.tex (Instructors only)(TEX | 7 KB)
• simiode.cls(CLS | 7 KB)
• SimiodeLogo.jpg(JPG | 271 KB)
• SpringSalePic.jpg(JPG | 147 KB)
• License terms

Authors

Author(s): Brian Winkel

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

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