Three Pendulums Connected by Two Springs
This Demonstration simulates the equations of motion for three rigid pendulums , , , with a spring attached from the end of to the end of and another spring attached from the end of to the end of . The system has three degrees of freedom and these are taken as the angle that each pendulum makes with the vertical. The three equations of motion were found using the Lagrangian method and solved numerically in their nonlinear form using the built-in Mathematica function NDSolve. Damping and friction are assumed to be negligible. You can adjust the masses of the pendulums, the initial conditions, and the spring stiffness coefficients. The Demonstration runs for 20 seconds and then starts over again from the beginning; you can adjust the speed with a slider. The kinetic and potential energy levels are displayed at the top as the system runs. The total energy remains constant. When you set the spring stiffness to zero, the spring is removed and the bar becomes a freely moving physical pendulum. All units are in SI.