Simple harmonic motion describes the vibration of atoms, ... Drawn out on a graph, the up-and-down motion of the ball over time can be illustrated as a smooth, ...

But for now, it's helpful just to see the connection here: For an object in simple harmonic motion, the graph of its position versus time is a wave. Which is why the swaying of the Millennium ...

Include a graph of total energy as a function of time for all three methods. Is energy conserved? At what starting angle does the pendulum not agree with a simple harmonic motion model?