ODE II Quiz
Part 1
Write the equations for the orbit problem in state vector notation by defining X and f(X,t).
Part 2
The Wilberforce pendulum consists of a mass suspended by a long spring. The mass is free to turn about its vertical axis as well as oscillate up and down. It oscillates vertically and torsionally. If we let z represent the vertical position of the mass m and θ be angle of rotation of the mass, then the equations of motion for the system are
where I is the moment of inertia of the mass, k is the spring constant for the vertical motion, κ is the constant for the torsional motion, and α specifies the coupling between the two modes of oscillation. Write a program using odeint to solve this system of ODEs and plot z and θ on the same graph. Let m = 0.5 kg, I = 1.0 × 10-4 kg m2, k = 5 N/m, κ = 1.0 × 10-3 N m, and α = 1.0 × 10-2 N. Show that for these particular values of the constants the motion periodically alternates between being purely vertical and purely torsional.