Consider a pendulum with a bob of mass m attached to a rigid but massless rod with length L. Which equation describes the motion of the bob with respect to the vertical?
Let's take the easy route for the moment.
¨θ≈−gLθ
What is the general solution to: ¨θ≈−ω2θ?
OMGBBQPIZZA
Nature tends to minimize energy
Have you worked with phase space before?
Now that we have sketched ⟨˙x,˙v⟩=⟨v,0⟩...
Sketch ⟨˙x,˙v⟩=⟨0,−x⟩ in phase space.
What about ¨x=−sinx?