There is a function that derives the equations of motion for a pendulum attached to a cart. The cart moves along the x-axis.and the point of attachment of the pendulum is on the x-axis. The coordinates of the point of attachment are denoted (u,0).

Modify this function by adding a spring attached to the cart and figure out the new equations of motion. The spring lies along the x-axis.

Things are arranged so the the spring is at its equilibrium when the point (u,0) is (0,0). Thus, the force exerted by the spring is given by Hooke's law as F = -ku, where k>0 is a constant that measures the stiffness of the spring.

To get the new Lagrangian, you need to add one potential energy term to the Lagrangian to account for the spring.

Write a Python program to solve the equations of motion numerically with odeint, and then display an animation to show the motion of the system. Make it easy to change the program to change the parameters and initial conditions.