**Course Title:** MATLAB Programming: Applications in Engineering, Data Science, and Simulation **Section Title:** Simulink and System Modeling **Topic:** Design and simulate a dynamic system using Simulink, and analyze the results.(Lab topic) **Objective:** In this lab topic, you will learn how to design and simulate a dynamic system using Simulink. You will create a new Simulink model, add blocks to build a dynamic system, simulate the system, and analyze the results. **Prerequisites:** You should be familiar with the fundamentals of Simulink, including building block diagrams for dynamic systems and simulating continuous-time and discrete-time systems. **Software Requirements:** You will need to have MATLAB and Simulink installed on your computer. **Step 1: Create a New Simulink Model** * To create a new Simulink model, go to File > New > Model. This will open a blank workspace where you can create your model. * Rename the model by going to File > Save As and giving your model a unique name. **Step 2: Add Blocks to Build a Dynamic System** * For this example, we will create a simple harmonic oscillator. The equation that describes a simple harmonic oscillator is: `x''(t) + (k/m) * x(t) = 0` where `x(t)` is the position of the oscillator, `x''(t)` is the acceleration, `k` is the spring constant, and `m` is the mass. * To build this system in Simulink, you will need the following blocks: + Integral (Continuous) block to integrate the acceleration to get the velocity + Derivative (Continuous) block to differentiate the position to get the velocity + Gain block to represent the spring constant `k` and the mass `m` + Sine Wave block to provide an input signal * Search for and drag these blocks from the Simulink Library Browser into your model. **Step 3: Configure the Blocks** * Configure the Integral (Continuous) block: + Go to the Parameters tab and set the Initial condition to 0. * Configure the Derivative (Continuous) block: + Go to the Parameters tab and set the Initial condition to 0. * Configure the Gain block: + Go to the Parameters tab and set the Gain to `k/m`. * Configure the Sine Wave block: + Go to the Parameters tab and set the Amplitude to 1 and the Frequency to 1 Hz. **Step 4: Connect the Blocks** * Connect the blocks to build the dynamic system: + Connect the Sine Wave block to the input of the Gain block. + Connect the output of the Gain block to the input of the Derivative (Continuous) block. + Connect the output of the Derivative (Continuous) block to the input of the Integral (Continuous) block. + Connect the output of the Integral (Continuous) block to the output of the system. **Step 5: Simulate the System** * To simulate the system, go to the Simulation tab and set the Stop time to 10 seconds. * Click the Run button to start the simulation. **Step 6: Analyze the Results** * To analyze the results, go to the Scopes tab and set the Scope to display the output of the system. * Click the Run button to start the simulation. * Observe the output of the system and see how the position and velocity of the oscillator change over time. **Real-World Applications:** * Dynamic systems are used in a wide range of fields, including physics, engineering, and economics. * For example, in physics, dynamic systems are used to model the motion of objects in space. * In engineering, dynamic systems are used to model the behavior of electronic circuits and control systems. * In economics, dynamic systems are used to model the behavior of markets and economies. **References:** * For more information on Simulink, see the [Simulink Documentation](https://www.mathworks.com/help/simulink/index.html). * For more information on dynamic systems, see the [Wikipedia article on dynamical systems](https://en.wikipedia.org/wiki/Dynamical_system). * For more information on simple harmonic oscillators, see the [Wikipedia article on simple harmonic oscillators](https://en.wikipedia.org/wiki/Simple_harmonic_motion). **Leave a comment/Ask for help:** * After completing this lab topic, please leave a comment below if you have any feedback or need help with any part of the topic. * Please provide any additional resources or references that you used to complete this lab topic. What's next? In the next topic, we will learn about "Introduction to differential equations and MATLAB's ODE solvers" from Solving Differential Equations with MATLAB.