State-space model of a mass-spring system with Coulomb friction

Chang Duan, Prairie View A & M University, Mechanical Engineering

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Initial Publication Date: October 7, 2025

Summary

This activity is for students enrolled in the "Dynamic Systems and Control" course who are learning "State Space Approach" for modelling and analysis. The system is a single mass and spring system with an initial displacement. The mass is placed on the ground and is subjected to Coulomb friction. The teacher will guide the students through the process of modelling the system using the state space approach, then simulating it using Simulink and plotting the displacement of the mass with respect to time.

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Learning Goals

1. Students will reinforce the concept of modeling dynamic systems using the state-space approach. Specifically, they will turn ordinary differential equations into state-space models.

2. Students will learn how to use Simulink to simulate a dynamic system with a state-space model, how to handle inputs, outputs, and nonlinearities etc. They will learn to plot and how to adjust Simulink settings to improve the smoothness of the graph.