Spring Pendulum Simulation using Lagrangian Mechanics in MATLAB | Modeling + Animation + Plotting

This project presents a complete dynamic modeling and simulation of a Spring Pendulum system using Lagrange’s equations in MATLAB. From system derivation to graphical animation, this simulation allows you to visualize both the motion and angular displacement of the pendulum suspended on a spring.

Perfect for engineering students, control system learners, and anyone exploring dynamic simulations using energy-based modeling.

🎯 What's Included:

✅ Fully functional MATLAB Script (.m)

✅ Lagrangian equation modeling with derivations

✅ Real-time 2D animation of spring-pendulum motion

✅ Angular displacement vs time plotting

✅ Kinetic & potential energy visual representation

✅ Clean and fully-commented code

✅ Easy to edit and reuse for academic or research projects

📚 Concepts Covered:

Spring-Pendulum system dynamics

Lagrangian mechanics (T – U)

Euler-Lagrange equation implementation

Real-time trajectory animation

MATLAB graphics and simulation techniques

📽️ Bonus:

Ideal for control system courses, physics projects, and simulation enthusiasts!

💬 Need Help?

For queries, customization, or collaboration, feel free to contact:

📧 mregnineer294@gmail.com

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📷 Instagram: @engrprogrammer2494

▶️ YouTube: @engrprogrammer