This Demonstration models the dynamical behavior of a pendulum connected to a cart that is in turn attached to a spring The path of the pendulum bob and the position and speed of the cart and the pendulum can be traced as you vary the parameters of the system The springcartpendulum system has two degrees of freedom the horizontal position of the cart and pendulum and the angle between the pendulums rod and the vertical In the absence of friction we have the following equations of motion is acceleration due to gravity