1. a. Consider the Duffing oscillator equation with no forcing
y ' = v
v ' = y – y3.
What are the equilibrium points for this system?
b. Show that this system is Hamiltonian with Hamiltonian function
H(y, v) = v2/2 – y2/2 + y4/4.
c. Sketch the level curves of this Hamiltonian function.
d. Describe the motion of the slender steel beam in the different cases that arise.