Mass-Spring-Damper Systems

Interactive courseware module that addresses the fundamentals of mass-spring-damper systems taught in mechanical engineering courses.

Mass-Spring-Damper Systems

Curriculum Module
Created with R2020b. Compatible with R2020b and later releases.

Description

This curriculum module contains interactive live scripts and Simulink® models that explore mass-spring-damper systems. Students learn to create and work with mass-spring-damper models in guided activities. These techniques are motivated by two applications: tuning the damping of a vehicle’s suspension and analyzing a building’s response to an earthquake. Throughout the module, students apply Simulink models to study the dynamics of the physical systems. In the final lesson, students identify the resonant frequencies of a mass-spring-damper building model by computing the power spectrum of a displacement signal. These lessons can be used as part of a lecture, as activities in an instructional setting, or as interactive assignments to be completed outside of class.

Learning Goals

• Construct free body diagrams and derive the equations of motion for mass-spring-damper systems
• Relate the mass, spring, and damper to their corresponding components in a physical system
• Create models that solve ordinary differential equations in Simulink
• Use the Symbolic Math Toolbox to help create Simulink models
• Complete Simulink mass-spring-damper models with 1, 2, and n degrees of freedom
• Relate parameter values to the dynamics of mass-spring-damper systems
• Tune the damping of a vehicle suspension model to meet requirements
• Identify the resonant modes of a mass-spring-damper building model

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Suggested Prework

MATLAB Onramp – a free two-hour introductory tutorial that teaches the essentials of MATLAB.
Simulink Onramp – a free three-hour introductory tutorial that teaches the essentials of Simulink.

Details

massSpringDamper.mlx, massSpringDamperSoln.mlx
An interactive lesson that teaches how to model a single mass-spring-damper in Simulink. Students apply their knowledge to tune the damping of a vehicle’s suspension system.

doubleMassSpringDamper.mlx, doubleMassSpringDamperSoln.mlx
An interactive lesson that teaches how to model a double mass-spring-damper in Simulink. Students apply their knowledge to identify the resonant frequencies present in a two-story building model.

multipleMassSpringDamper.mlx, multipleMassSpringDamperSoln.mlx
Students practice more advanced skills in this lesson, such as vectorizing a Simulink model and using the Spectrum Analyzer block to compute the power spectrum.

models/
Simulink models used during the guided activities. Starter models and their completed solutions are included.

Products

MATLAB®, Symbolic Math Toolbox™, Simulink

License

The license for this module is available in the LICENSE.TXT file in this GitHub repository.

Educator Resources

• Featured Courseware
• Teach with MATLAB and Simulink
• MATLAB Grader

Have any questions or feedback? Contact the MathWorks online teaching team.

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