Modeling and Analysis of Physical Systems Dynamics

Dynamic systems are everywhere—from simple thermostats to complex aerospace mechanisms. Understanding how these systems respond to inputs and disturbances over time is essential for effective engineering design and control. This course provides a solid foundation in the principles of dynamic system analysis. You will move from foundational physics laws to creating mathematical models and interpreting system responses, preparing you for advanced study in control theory and computational simulation. What you'll learn: * Understand the fundamental laws (e.g., Newton's laws, Kirchhoff's laws) used to derive mathematical models for various physical systems. * Apply linear graph theory and free-body diagrams to systematically construct governing equations for complex systems. * Practice solving first-order and second-order differential equations to determine transient and steady-state system responses. * Analyze system behavior using both transfer functions and modern state-space representation methods. * Determine system stability using classical techniques like the Routh-Hurwitz criterion. * Configure basic computational models for simulating dynamic responses when analytical solutions are impractical. The course begins by defining key terminology and modeling approaches across different energy domains. It progresses through techniques for solving linear ordinary differential equations and analyzing system behavior in both the time and frequency domains. This course is designed for absolute beginners interested in engineering, physics, or applied mathematics. No prior knowledge of system dynamics is required, only basic calculus understanding. Start building your understanding of how the physical world moves and reacts today.