# “Mass-Spring-Damper Systems” Courseware

## Course Materials Include:

#### Mass-Spring-Damper Systems

This curriculum module contains interactive MATLAB live scripts and Simulink models that explore mass-spring-damper systems. Throughout the module, students apply Simulink models to study the dynamics of the physical 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. 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.

The live scripts include:

• massSpringDamper.mlx: 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: 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: lesson that enables the practice of more advanced skills; students identify the resonant frequencies of a mass-spring-damper building model by computing the power spectrum of a displacement signal

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 Symbolic Math Toolbox to help create Simulink models.
• Complete Simulink mass-spring-damper models with one, two, 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.

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