Solid Pendulum with a Spring-Mass System

This Demonstration describes the dynamics of a solid pendulum in which a massive bob slides back and forth over a massless and smooth thin tube attached to the bottom of a pendulum bar. The bob is attached to the end of a spring. When the bob hits the ends of the tube, it bounces back; the ends are assumed to be perfectly elastic. The two equations of motion for the bob and the pendulum bar are derived using the Lagrangian method, which is solved numerically by Mathematica's built-in function NDSolve. The spring is anchored to the left edge of the tube, assumed to be massless, and can move in only one direction along the length of the tube. Setting the spring stiffness to zero effectively removes the spring, allowing the bob to oscillate freely.