Vibrations: Torsional System | Tip Mass & Helical Spring–EOM & Linearization via Lagrange’s Equation

This video presents a torsional vibration problem where a tip mass is attached to a helical (translational) spring, modeling a simplified torsional system. Unlike the previous case, the pendulum bar mass is ignored, focusing on the rotational motion of the tip mass. The equation of motion (EOM) is derived using Lagrange’s Equation, and the nonlinear EOM is linearized using the small-angle approximation to simplify analysis.

🔹 Key Topics Covered:
✅ Modeling a torsional system with a tip mass and helical spring
✅ Applying Lagrange’s Equation to derive the nonlinear EOM
✅ Linearizing the equation using the small-angle approximation
✅ Understanding stiffness contributions from translational and rotational motion
✅ Interpreting the natural frequency and system behavior

📖 Related Topic in Mech Prof. Lee’s OER Vibrations Textbook:
Topic 03 – Free Vibration of Single DOF: Undamped Torsional System
https://eng.libretexts.org/Courses/Ca...

This video is ideal for engineering students, researchers, and professionals looking to strengthen their understanding of torsional vibrations, energy-based equation derivation, and small-angle approximations for linearization.

📌 Watch now to master Lagrange’s approach to torsional vibration analysis and equation linearization!